Trading Systems and Money Management : A Guide to Trading and

Transcription

TRADING SYSTEMS AND
MONEY MANAGEMENT
Other Books in The Irwin Trader’s Edge Series
Techniques of Tape Reading by Vadym Graifer and Christopher Schumacher
Quantitative Trading Strategies by Lars Kestner
Understanding Hedged Scale Trading by Thomas McCafferty
Trading Systems That Work by Thomas Stridsman
The Encyclopedia of Trading Strategies by Jeffrey Owen Katz and
Donna L. McCormick
Technical Analysis for the Trading Professional by Constance Brown
Agricultural Futures and Options by Richard Duncan
The Options Edge by William Gallacher
The Art of the Trade by R. E. McMaster
TRADING SYSTEMS AND
MONEY MANAGEMENT
A Guide to Trading and
Profiting in any Market
THOMAS STRIDSMAN
McGraw-Hill
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DOI: 10.1036/0071435654
Want to learn more?
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This book is dedicated to my entire family in general,
but to the little ones in particular. My niece Matilda and
my nephews Erik and Albin, you make me laugh. One
can only hope that you and your friends get to have a
glass of beer…
Also, with the most sincere hopes for a full and speedy
recovery for my mother after her severe traffic accident.
This page intentionally left blank.
DISCLAIMER
The entire contents of this book, including the trading systems and all the analysis techniques to derive and evaluate them, is intended for educational purposes
only, to provide a perspective on different market and trading concepts. The book
is not meant to recommend or promote any trading system or approach. You are
advised to do your own research to determine the validity of a trading idea and the
way it is presented and evaluated. Past performance does not guarantee future
results; historical testing may not reflect a system’s behavior in real-time trading.
For more information about this title, click here.
CONTENTS
INTRODUCTION xvii
ACKNOWLEDGMENTS xxi
PART ONE
HOW TO EVALUATE A SYSTEM 1
Performance Measures 4
Chapter 1
Percentages and Normalized Moves 7
About the Costs of Trading 12
Chapter 2
Calculating Profit 15
Average Profit per Trade 16
Average Winners and Losers 20
Standard Deviation 22
Distribution of Trades 25
Standard Errors and Tests 28
Other Statistical Measures 30
Time in Market 31
ix
Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
Contents
x
Chapter 3
Probability and Percent of Profitable Trades 35
Calculating Profitable Trades 35
The Difference Between Trades and Signals 43
Chapter 4
Risk 47
Calculating Risk 48
A Sample Strategy Analysis 51
Chapter 5
Drawdown and Losses 57
Drawdown Compared to Equity 58
Drawdown Compared to the Market 59
Mean–Median Comparisons 60
Types of Drawdown 63
Chapter 6
Quality Data 67
A Scary Futures-Market Example 71
Understanding Profitability 76
PART TWO
TRADING SYSTEM DEVELOPMENT 79
Chapter 7
TradeStation Coding 83
Export Code 86
Comments on the Code 89
The Exported Data 91
Initial Description of the Systems 95
Chapter 8
Hybrid System No. 1 97
Suggested Markets 97
Contents
xi
Original Rules 97
Test Period 98
Test Data 98
Starting Equity 98
System Pros and Cons 98
Revising the Research and Modifying the System 99
TradeStation Code 102
Chapter 9
RS System No. 1 105
Original Rules 105
Test Period 106
Test Data 106
Starting Equity 106
Chapter 10
Meander System V.1.0 113
Original Rules 114
Test Period 114
Test Data 114
Starting Equity 114
Chapter 11
Relative Strength Bands 123
Original Rules 124
Test Period 124
Test Data 124
Starting Equity 124
Contents
xii
Chapter 12
Rotation 137
Original Rules 138
Test Period 138
Test Data 138
Starting Equity 138
System Analysis 138
Chapter 13
Volume-weighted Average 153
Original Rules 154
Test Period 154
Test Data 154
Starting Equity 154
Chapter 14
Harris 3L-R Pattern Variation 163
Original Rules (Long Trades Only) 164
Test Period 164
Test Data 164
Starting Equity 164
Contents
xiii
Chapter 15
Expert Exits 173
Original Rules (Reverse the Logic for Short Trades) 174
Test Period 174
Test Data 174
Starting Equity 174
Chapter 16
Evaluating System Performance 185
PART THREE
STOPS, FILTERS, AND EXITS
191
Chapter 17
Distribution of Trades 193
Chapter 18
Exits 201
Limiting a Loss 201
Taking a Profit 203
End of Event 204
Money Better Used Elsewhere 205
Chapter 19
Placing Stops 207
Percent Stops 209
Volatility 210
Surface Charts 212
Contents
xiv
Chapter 20
Adding Exits 219
Surface Chart Code 220
Hybrid System No. 1 226
Stop-loss Version 226
Trailing-stop Version 233
Meander System, V.1.0 237
Volume-weighted Average 241
Harris 3L-R Pattern Variation 245
Expert Exits 248
Uncommented Bonus Stops 250
Chapter 21
Systems as Filters 255
RS System No. 1 as the Filter 260
Relative-strength Bands as the Filter 262
Rotation as the Filter 266
Chapter 22
Variables 271
Chapter 23
Evaluating Stops and Exits 281
Contents
xv
PART FOUR
MONEY MANAGEMENT 287
Chapter 24
The Kelly Formula 289
Chapter 25
Fixed Fractional Trading 295
Chapter 26
Dynamic Ratio Money Management 305
Building a Sample Spreadsheet 310
Chapter 27
Spreadsheet Development 325
Money Management Export Code 337
Chapter 28
Combined Money Market Strategies 343
Strategy 1
Strategy 2
Strategy 3
Strategy 4
Strategy 5
Strategy 6
Strategy 7
Strategy 8
Strategy 9
Strategy 10
Strategy 11
Strategy 12
345
349
352
354
356
358
359
362
363
365
366
369
Contents
xvi
The Counterpunch Stock System 374
Rules 376
Money Management 376
Test Period 376
Test Data 377
Starting Equity 377
System Analysis 377
Chapter 29
Consistent Strategies 379
Conclusion 382
INDEX 385
INTRODUCTION
“This is Wall Street, no act of kindness will pass unpunished.”
— Unknown
A
s an editor, writer, and technical analysis expert first for Futures magazine and
later Active Trader magazine, I realized that although there are plenty of technical
analysis books in general and on rule-based trading in particular, they were all saying the same thing and not bringing any new thinking into the subject. This is especially true when it comes to the intricate topic of how to build and evaluate a trading
system so that it remains as robust and reliable when traded together with a professional money management regimen in the real world, as it seemed to be when tested on historical data.
In an effort to do something about this, I first wrote Trading Systems That
Work (McGraw-Hill, 2000), which focused on longer-term systems on the futures
markets, and now Trading Systems and Money Management, which focuses on
short-term systems in the stock market. Both books combine featured systems with
a fixed fractional money management regimen to maximize each system’s profit
potential, given the trader’s tolerance for risk.
To combine a mechanical trading system (the rules for where and when to buy
and sell a stock or commodity) with any money management strategy (the rules for
how many to buy and sell, given the trader’s risk–reward preferences and the behavior of the markets), is not as easy as taking any system, applying it to any market
or group of markets, and deciding on not risking a larger amount per trade than
what your wallet can tolerate.
Instead it’s a complex web of intertwining relationships, where any change
between two variables will alter the relationship between all the other variables.
And, as if that’s not enough, the strategy should be dynamic enough to mechanically self-adjust to the ever-changing market environment in such a way that the
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xviii
Introduction
risk–reward potential remains approximately the same for all markets and time
periods.
This book is for those traders who haven’t been able to pinpoint what is missing to make the complete strategy larger than the sum of its parts. If you allow me
to take a guess, I’d guess that what you feel is keeping you from succeeding as a
trader is the overall understanding for how it all ties together and what really constitutes a more “sophisticated” strategy with a higher likelihood for success than
the ones you’re currently using. The way I see it, to simplify things, the development process could be divided into a few building blocks:
First, we need to learn what we need to measure to achieve robustness and
reliability. Second, we need to learn to formulate and test the logic for the entry
(and possibly also some sort of filtering technique). Third, we must understand and
test different types of exits. The last point of actual research is to apply and test the
money management according to our risk preferences.
The first part of the book will show you how to measure a system’s performance to make it as forward-looking as possible. By forward-looking we mean
that the likelihood for the future results resembling the historical results should be
as high as possible. To do this, you will need to know the difference between a
good working system and a profitable system and which evaluation parameters to
use to distinguish between the two.
The emphasis will lie on making the system work, on average, equally as
well on a large number of markets and time periods. We also will look at other
common system-testing pitfalls, such as working with bad data and not normalizing the results. Another important consideration is to understand what constitutes
realistic results and what types of results to strive for. A lot of the analysis work
will be done in TradeStation and MS Excel.
In the second part, we will take a closer look at the systems we will work
with throughout the rest of the book. All eight systems have previously been featured in Active Trader magazine’s Systems Trading lab pages. The systems are
selected only as good learning experiences, not for their profitability or trading
results. We will look at the systems one at a time and determine how we can modify them to make them more robust and forward-looking.
All changes will be based on logic and reasoning, rather than optimization
and curve fitting, and are aimed to improve the system’s average performance over
a large number of markets and time periods, rather than optimizing the profits for
a few select markets. The working premise will be, the better we understand the
logic behind the system and the less complex the system, the more we trust it will
function as well in the future as it has in the past. For this, we will do most of the
work in MS Excel, which means we need to learn how to export the data from our
analysis software of choice.
Usually when I build a system, I don’t count the stop-loss and exit rules to
the core system logic. In Part 3 we therefore substitute all the old exit rules for all
Introduction
xix
systems with a set of new rules, optimized to work on average equally as well on
all markets at all times. To do this, we need to understand what types of exits are
available, how to evaluate them, and how to avoid falling into any of the problems
that adhere explicitly to the evaluation of exits. However, even though the larger
part of Part 3 deals explicitly with stops and exits, the methods used (such as analyzing the results with a surface chart in MS Excel) also are applicable to other
parts of the system-building process.
At the end of this part, we also will take a look at how to increase performance by adding a relative-strength or trend filter. Decreasing the number of trades
might decrease the performance for any individual market, but by making room
for more trades in more markets, we can increase performance thanks to a higher
degree of diversification.
The last part of the book will tie it all together by applying a dynamic ratio
money management (DRMM) regimen on top of all the trading rules. With
DRMM, all markets traded will share the same account, so that the result for one
market is dependent on the results from all other markets and how much we decide
to risk in each trade. Also, the number of possible markets to be traded simultaneously and the amount risked per share in relation to the total amount risked of
account equity will vary with the conditions of the markets.
Using DRMM, we also can tailor the amount risked per trade to fit our exact
tolerance for risk given the system’s statistical characteristics and expected market
conditions. In this case, instead of optimizing the equity growth, we will optimize
the smoothness of the equity curve. Even with this modest goal, we will achieve
results far higher and better than comparable buy-and-hold strategies. But before
we set out to test the systems using DRMM, in our custom-made Excel spreadsheet, we will learn exactly how DRMM works with all its mathematical formulas
and why it is the supreme money management method.
However, when moving back and forth between the different steps in the
development process we have to understand that any little change under any of
these categories also will alter the characteristics produced by the others. Therefore,
building a trading system is a never-ending task of complex intertwining dynamics
that constantly alter the work process. This really creates a fifth element that runs
through the entire process as a foundation for the other elements to rest on.
The fifth element is the philosophic understanding of how all the other parts
fit together in the never-ending work process already mentioned. If anything, I
hope that what makes this book unique is the overall understanding for the entire
process and the way it will force you to think outside of the conventional box.
Developing a trading strategy is like creating a “process machine,” in which
each decision automatically and immediately leads to the next one, and next one,
and next one … producing a long string of interacting decisions forming a process
with no beginning or end. I further believe it is paramount to look at both the
development and the execution of the strategy in the same way.
xx
Introduction
The purpose of this book is not to give you the best ready-made systems, but
to show you how to go about developing your own systems—a development process
that eventually and hopefully will allow you to put together a trading strategy that is
a long-term work process as opposed to a series of single, isolated decisions.
The advantage of the concept of a work process, in comparison with decision,
is that rule-based trading can be understood as a form of problem solving, using the
four P’s of speculation: philosophy, principles, procedures, and performance.
The emphasis in this book seems to be on the principles, procedures, and performance, but while reading we also need to at least try to understand the philosophy behind it all, because it is the philosophy that ties it all together and explains
the value of the suggested principles and procedures in the rest of the book. That
is what this book really is about. Good luck with your studying and trading.
ACKNOWLEDGMENTS
My most heartfelt gratitude to Dan and Maryanne Gramza.
Many thanks to Nelson Freeburg and his family.
My most sincere wishes for the future success of Active Trader magazine and
its crew, Phil, Bob, Mark, Laura, Amy, and that other weird guy—you’re the best.
There are no better friends than my dear friends Jill in Rockford, IL and Pär
in Västerås, Sweden. Thanks for putting up with me.
To Robert, Brad, and the rest of the bunch at Rotella Capital: It’s a true honor
to work with and for you all. A special thanks to Rafael Molinero, for invaluable
help with this book.
PART
ONE
How to Evaluate a System
A
t the time of this writing, there’s a TV commercial running on several of the
business and news channels. The commercial is for an online direct-access brokerage company that claims to give you better fills than the brokerage company
your cubicle-sharing colleague is using. The plot is as follows: Guy 1 proudly tells
Guy 2 that he just bought 300 shares of XYZ for $25.10, only to hear that Guy 2
just bought 200 shares of the very same stock for $25.05. Of course, this 5-cent
difference makes Guy 1 all upset, and Guy 2 takes advantage of it by smugly alerting everyone to “Tom’s unfortunate stock purchase” over the company intercom
system.
Obviously, the purpose of the commercial is to make us believe that the most
important thing in trading isn’t a long-term plan, involving such “mundane” factors as the underlying logic of your system and numbers of shares to trade, but only
to get a 5-cent better fill than your cubicle buddy.
This is a good example of how many companies within the investment and
trading industry don’t know what they’re talking about. Or if they do, they want to
fool you into focusing on the wrong things, because if you were focusing on the
right things, their services would be obsolete. I really don’t know which is worse.
Basically, two types of companies try to feed on your trading. The brokerage
companies try to make you believe that a 5-cent better fill makes all the difference
in the world. The newsletter and market-guru companies claim that only their topand-bottom-picking system will help you squeeze those extra 10 cents out of each
trade, which will take your account equity to astronomical heights (or at least,
finally make you profitable).
The truth is those few extra cents matter little in the end. To understand this,
let’s return to the guys in the cubicle and assume that XYZ indeed started to move
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PART 1 How to Evaluate a System
in the anticipated direction. If that were the case, would you rather be Guy 1 or
Guy 2? I don’t know about you, but with the stock moving favorably, I’d rather own
300 shares bought at $25.10, than 200 shares bought at $25.05. Why? Because, if
the stock moves in the anticipated direction, the profit from the 300 shares will
soon—very soon—outweigh the profit made from the 200 shares. How soon?
Only 10 cents later, at $25.20!
Now, because a TV commercial is a make-believe world in the first place,
let’s add another few make-believe assumptions to it. First, let’s pretend that both
guys had $25,000 on their trading accounts going into the trades, that XYZ
continues to trend higher, and that both guys got out at 30. How much money did
each guy make? Guy 1 made $1,470 [(30 25.10)*300], while Guy 2 made $990
[(30 25.05)*200].
Further, what if both guys were able to make 10 such trades in a row? How
much money would each one of them have in his trading account after such a run?
Guy 1 would have $39,700 (25,000 [1,470*10]), while Guy 2 would have
$34,900 (25,000 [990*10]). Thus, over this 10-trade sequence, Guy 1 would
have made $4,800 more than Guy 2.
As a final assumption in this make-believe world, let’s back up to the first
trade and assume that Guy 1, instead of always buying 300 shares, had continued
to invest 30 percent [(25.10*300)/25,000] of his account balance in each trade,
while Guy 2, the smug nickel-and-dimer that he is, continued to buy 200 shares
per trade over the entire sequence of 10 trades. How much more would Guy 1 have
on his account, compared to Guy 2? Guy 1 would have a total of $44,149, which
would be $9,249 more than Guy 2.
So what have we learned from this? The answer is, while it is unrealistic to
assume 10 such winning trades in a row (it happens every so often, but it’s not a
particularly realistic assumption), managing your trade size is way more important
than chasing a nickel here and a dime there on your entry and exit levels. This is
one of two important points I hope to get across in this book.
However, to be able to “optisize” the amount to risk and invest in each trade,
you need to have a trading system you can trust and that allows you to do so. You
can’t do this without fully understanding the second most important point this
book tries to convey. To illustrate the second point, let’s change the topic completely:
Picture a cheetah on the African savannah. The cheetah is one of my favorite
animals. It’s a highly specialized, lean, mean, killing machine that can outrun just
about anything and anyone. Its limber and muscular body and graceful moves ooze
self-confidence. As a metaphor for a good trading system, however, the cheetah
sucks. The reason is that it’s simply too specialized in hunting and killing a certain
sized prey in a certain natural habitat.
If the prey were slower but larger, the cheetah could outrun and catch it more
easily, but waste time killing it and run a larger risk of being killed itself. If the
3
prey were smaller but faster, the amount of energy gained from consuming it
wouldn’t make up for the amount of energy wasted hunting it down. The truth is
that if the animals that make up the better part of a cheetah’s diet disappeared, so
would the cheetah. The same will happen if the environment changes and becomes
more rocky, bumpy, or hilly, or if the forest takes over the savannah, so that the
cheetah can’t utilize its number-one hunting weapon—its speed. Thus, the cheetah
is too dependent on its environment to survive in the long run.
Similarly, a trading system with the characteristics of a cheetah would cease
to work properly if and when the environment it operates in changes ever so slightly (and in a myriad of ways), and the only way for you to find that out is when
you’re already in a drawdown you can’t get out of. Therefore, it is paramount that
your systems can work in as many market environments as possible, or to use the
words of the analogy, find and catch its prey wherever possible, wasting as little
energy as necessary.
Now, this doesn’t have to mean that each system needs to work equally as
well in all conditions. It means that a system needs to work well enough to keep
you afloat, or at least out of disaster in less favorable conditions, while waiting
for the good times to reappear. And the only way to achieve that is to familiarize the system with the less favorable market environments during the research
and building process. More specifically, it means that you should let the system’s final parameter settings be influenced by the best settings for less favorable conditions, no matter if those less favorable conditions actually produce a
profit or not.
For example: Picture a moving average cross-over system, with a four-day
short average and a 25-day long average, that produces great results in one market
(or market condition), but terrible results in another. For a second market (condition), the best, but still negative, results might come from a 12-day short average
and an 18-day long average. In that case, you might be better off, in the long run
and on average, with a final setting of nine days for the short average and 20 days
for the long average, which still might produce good results in the first market and
a slight loss in the second market.
Whether you then decide to trade both markets or only the profitable one
depends on other considerations and what you’re trying to achieve with this particular system in the first place. Assuming you’re only trading the profitable market, at least results won’t be as bad as they could have been when the profitable
market starts to behave as the unprofitable one, which you won’t discover until it’s
too late.
If, on the other hand, you trade both markets, you might lower your profits
initially because of the bad performance of the second market. But just as the first
market might start to behave as the second market, the opposite is true as well, and
when that happens, profits will increase. Trading more than one market most likely also will lower the fluctuations of the results and make the system less risky to
4
trade over the long haul. Furthermore, a market that is losing money by itself can
still add positively to your equity when traded together with other markets in a
portfolio. It all depends on its correlation with the other markets. Or, to put it in
less scientific terms: It all depends on how and when each market zigs and zags in
relation to all the other markets.
When I build a system for the Trading Systems Lab pages in Active Trader
magazine, I usually test it on 30 to 60 markets, not expecting it to be profitable on
more than two-thirds of those. Preferably, I also want it to be only marginally profitable on the profitable markets, but, by the same token, only marginally unprofitable on the losing markets. Also, the fewer the markets that stick out (whether for
good or bad), the better the system, as far as I’m concerned.
Hopefully, in the end, this will mean that all markets will go through both
good and bad periods, but at each instance there will be, on average, more markets
doing well than doing badly. Also, when one market moves from good to bad,
which is easily done, most likely one or two markets will move the other way to
pick up the slack.
So, which living creature do I want my trading systems to resemble? The
cockroach, which can stay alive a week on the fat left behind by a fingerprint, with
almost no concern for the environment or habitat.
PERFORMANCE MEASURES
Have you noticed that the financial press and television frequently report the daily
price changes for a stock or an index in percentage terms, together with the dollar
changes? Believe me, this has not always been the case. When I moved to Chicago
from Sweden, back in 1997, hardly anyone presented the percentage changes, and
I was just amazed at how the supposedly financially most sophisticated country in
the world didn’t know how to calculate percentages.
Everyone I tried to talk to about this just stared at me with blank eyes, and I
found myself in constant arguments with both common men and distinguished
system designers and money managers about why doing the analysis in percentage terms instead of dollars will result in better, more reliable, forward-looking
trading systems. Most, however, seemed to be too blinded by the almighty dollar
to understand what the hell I was talking about.
So, while writing for Futures magazine, I decided to start my own little percentage crusade by stressing the importance of measuring a price change in relation to the price level around which the change took place. After two years of
doing that, I ended up writing a book on how measuring trading performance in
percentages pertains to systematic trading using mechanical trading systems in the
futures markets (Trading Systems That Work, McGraw-Hill, 2000).
As a senior editor for Active Trader magazine, I continued to stress the
importance of using relative rather than absolute measurement techniques. At the
5
time of this writing, things are getting better. People are beginning to understand
what the hell I’m talking about, although so far the financial press and television
haven’t dared to stress the relative change as the more valid of the two figures.
To be sure, the academic community and the big boys of Wall Street have
always known about this, although the academic community many times prefers to
work with logarithmic changes instead (as for example, in the Black–Scholes
options evaluation formula), which is essentially the same thing. Why they haven’t
stressed this to the average trader and investor is beyond me. Could it be that it provided them a good opportunity to make a buck at your expense?
CHAPTER
1
Percentages and Normalized Moves
You cannot evaluate a system properly—at least not during the research and building process—if you don’t look at the right evaluation measures. And to look at the
right evaluation measures, you need to know and do a few things before you can
get started.
Basically, you can go about doing it correctly in two ways. Unfortunately,
however, just buying the same amount of shares for all stocks you’re looking at,
not caring about the price of each stock at each instance, isn’t one of them.
Especially not if all you’re interested in is dollars made during the testing period.
Weird, you say: Isn’t that the sole purpose of my trading in the first place,
making as much money as I can, while losing as little as I can? Yes it is, but we
have to remember that there is a huge difference between testing a system on historical data and then trading it real-time on fresh, never before seen data.
When you’re testing a system, you’re doing just that. You’re testing it—not
trading it. It seems to me that many people believe that testing and trading is the
same thing. This is not so! Therefore, when you’re testing a system, you should
concern yourself less with how much money you could have made in the past.
Instead, you should concern yourself with how to make whatever testing results
you’ve got as repeatable as possible in the future.
Not until that is achieved should you concern yourself with hypothetical
profits. If the system also shows a profit, good: Now you can move on to the next
step and eventually start trading it live and for real, but only for as long as you
remember that the dollars made say nothing about the reliability of the system. As
I said, there are two ways of doing it correctly. The first way is to make all hypothetical trades with one share, or one contract only, no matter which market you’re
7
8
testing, how much the price might fluctuate for a specific market, or how many
markets you’re testing the system on. But—and this is the important part—instead
of measuring the results in dollars won or lost, the outcome of each trade should
be measured in percentage terms in relation to the entry price of the trade.
The second way is to vary the number of shares or contracts traded in such a
way that the number of shares increases as the price of the stock or the futures contract decreases. For example, if a stock is priced first at $100 and then $50, you
should test the system with twice as many shares when the stock is priced at $50
as compared to when it was priced at $100. You should do this no matter if that’s
what you would have done in real life or not. Using this technique, the results can
still be measured in dollars.
To illustrate why all this is important, let’s look at two examples, both of
them in the form of questions. (Hint: before you answer the questions, go back to
the beginning of this part and re-read the story about the two cubicle buddies and
“Tom’s unfortunate stock purchase.”)
Say that stock ABC currently is trading at $80, and a trading system that consistently buys and sells 100 stocks per trade shows a historical, back-tested profit
of $250,000 over 500 trades, for an average profit per trade of $500 and an average profit per share of $5. These results are to be compared to those of stock XYZ,
with a back-tested profit of $125,000, also over 500 trades, for an average profit
per trade of $250 and an average profit per share of $2.50. Over the entire testing
period, the price of XYZ has more or less constantly been half that of stock ABC.
Now, everything else aside, do the above numbers indicate that stock ABC is a better stock to trade with this system than stock XYZ?
(This reasoning can also be translated over to a stock split. For example,
say that stock QRS is trading at $90, and a trading system that consistently buys
and sells 100 stocks per trade shows a historical, hypothetically back-tested
profit of $150,000. Tomorrow, after the stock has been split 3:1 and the stock is
trading at $30, the historical, hypothetically back-tested profit has decreased to
$50,000. Does this mean that the system suddenly is three times as bad as the
day before?)
No, it does not: A stock that is priced at twice the value of another stock also
can be expected to have twice as large price swings, and therefore twice as high a
profit per share traded. If you look at the above numbers, you will see that a profit per share of $2.50 relates to a stock price of $40 in the same way that a profit
per share of $5 relates to a stock price of $80 (2.5 / 40 5 / 80 0.0625 6.25%). That is, in percentage terms, the profit per share is the same for both
stocks. (As for the stock-split example, it is easy to see that after the split, we will
need to trade the stock in lots of 300 shares per trade to make the new results comparable to the old presplit results.)
To make the same net profit trading stock XYZ as trading stock ABC, all you
need to do is to trade twice as many XYZ stocks in each trade as you would stock
CHAPTER 1 Percentages and Normalized Moves
9
ABC. And why shouldn’t you? If you can afford to buy 100 shares of a stock
priced at $80, for a total value of $8,000, then you also can afford to buy 200
shares of stock priced at $40, also for a total value of $8,000. If you say you can
only afford to buy 100 shares of a stock priced at $40, for a total value of $4,000,
then you can still equalize the results by buying only 50 shares of the stock priced
at $80, also for a total value of $4,000.
In the latter case, you won’t make as much money in the end, but the point is
that the dollars made are not a good indication of how good the system is or how
likely it is that it will hold up in the future. In real-life trading, obviously, other
considerations come into play when you decide how many shares to buy in each
trade, but we will get to that later in the book.
For now, we have to remember that we’re talking about how to build and evaluate a back-tested system, and during this process, we either need to adjust the
number of shares traded to the price of the stock in question (so that we always
buy and sell for the same amount), or buy and sell one share only (but measure the
results in percentage terms). Otherwise, we won’t place each trade in all markets
on the same ground, or equal weighting, as all the other trades in all the other markets. And if we don’t do that, we might come to a suboptimal conclusion, as this
second example shows.
If you can choose between buying two different stocks, one currently priced
at $12.50 and the other at $20, and you know for sure that the one priced at $12.50
will rise 1.75 points over the next couple of days, while the one priced at $20 will
increase 2.60 points (almost a full point more) over the same period, which one
would you buy? If you answer the one for $12.50, you probably have taken the
story about the cubicle buddies to heart and understand what I am hinting at.
If, however, you answered the one for $20, you probably are a little too anxious to chase that elusive dollar. If you stop and think for a second, you will realize that there is a greater return for you if you just do the math. In this case, the
price of the low-priced stock divided by the price of the higher-priced stock (12.5
/ 20) equals 0.625, or 5/8. Thus, if you plan to invest $10,000, you can buy either
500 $20 shares, or 800 $12.50 shares. If you buy 500 $20 shares, you will make a
profit of $1,300 (2.60 * 500), or 13 percent of the invested amount (1,300 / 10,000
0.13). If, on the other hand, you buy $10,000 worth of the $12.50 stock, your
profit will be $1,400 (1.75 * 800), or 14 percent of the amount invested (1,400 /
10,000 0.14).
If you think this difference isn’t that much to worry about, what if you could
chose between 20 trades like this for the rest of the year, being able to use the profits from all trades going into the next one? Then your initial $10,000 would grow
to $115,231 if you only bought the $20 stock, but to $137,435 if you only bought
the $12.50 stock. And what if you could do this for three years straight? Then your
initial $10,000 would grow to $15,300,534 if you only bought the $20 stock, but
to $25,959,187 if you only bought the $12.50 stock. A difference of more than
10
$10,000,000 after only 60 trades. Although these are exaggerated numbers, they
illustrate the point that it pays to take it easy and do the math before you jump into
a trade. And it is exactly this type of math you also need to do while researching
your systems. If for nothing else, wouldn’t it be cool to know how much richer you
are than your cubicle buddy, while five cents still is a significant amount of money
to him?
The key point I’m trying to get across here is that there is a vast difference
between a good system and a profitable system. The most profitable system
doesn’t have to be the best system or even a good system at all, with the best
entry and exit points, and traded at the lowest commission. Those things help,
but what is more important is that a good system is a system that works, on average and over time, equally as well on as many markets and market conditions as
possible. The trades produced by a very good system don’t deviate from their
average trade as much as they do for a not-so-good system. A good system can
always be turned into a more or less profitable system by being applied to the
right markets and by altering the number of shares or contracts traded in each
trade. A system that is only profitable on one or just a handful of markets can’t
be made more or less good by being applied to more (losing) markets, no matter how aggressively we’re trading it.
The better the system, the more likely it is to hold up in the future, when traded on real-time, never before seen data, no matter in which market or under which
market condition it is traded. The same does not hold true for a system that might
show a profit here and now, but only in one or a handful of markets. To find out if
a system is good or not, we need to measure its performance, either in percentage
terms trading one share only, or in dollar terms always investing the same amount.
Unfortunately, none of the market analysis and trading software packages of today
allow you to do this right off the bat.
Because of this, I prefer to work with TradeStation, which is the only off-theshelf program I know that allows you to write your own code to compensate for its
shortcomings. When I am working with a system for the Trading System Lab
pages in Active Trader magazine, I usually work in a two-step process.
For step 1, I attach the following code to the system that I’m working on,
with the normalized variable set to true. In this way, the system will always buy as
many shares as it can for $100,000, all in accordance with what we have learned
about buying or selling more shares according to the price of the stock. With this
piece of code in place, I can examine the results for each individual market using
TradeStation’s performance summary, which can look something like Figure 1.1.
At this stage of the research process, I’m basically just interested in getting a feel
for how many of the markets are profitable, and to get a feel for the profit factor,
the value of the average trade, and the number of profitable trades.
Step 2, which incorporates exporting the percentage-based changes into a
text file for further analysis in Excel, will be discussed more thoroughly later.
FIGURE
11
1.1
TradeStation performance summary.
Note: In the following code, the method for calculating the number of
futures contracts differs from how to calculate the number of stock shares. This has
to do with the limited life span of a futures contract and how you need to splice
several futures contracts together to form a longer time series. If you’re interested,
a more thorough discussion surrounding these specific problems is found in
Trading Systems That Work. For the purpose of this book, we will only touch on it
briefly again in Chapter 6.
{For TradeStation reports. Set Normalize(False), when exporting for Money
management.}
Variables:
{These variables can also be used as inputs for optimization purposes.}
Normalize(True), FuturesMarket(False), ContractLookback(20),
{Leave these variables alone.}
NumCont(1), NormEquity(100000), RecentVolatility(0);
12
If Normalize = True Then Begin
If FuturesMarket = True Then Begin
RecentVolatility = AvgTrueRange(ContractLookback);
NumCont = MaxList(IntPortion(NormEquity /
(RecentVolatility * BigPointValue)), 1);
End
Else
NumCont = MaxList(IntPortion(NormEquity /
Average(AvgPrice, ContractLookback)), 1);
End;
ABOUT THE COSTS OF TRADING
Although there is no way around the costs of trading in real life, you should not
concern yourself with slippage and commission in the initial stages of building
and researching a trading system. To understand why this is, we once again have
to remind ourselves that there is a big difference between building and researching a system and actually trading it.
When we’re back testing on historical data, we should not try to squeeze out
as many fantasy dollars or points as possible, but rather try to capture as many and
as large favorable moves as possible, no matter what the cost of trading happens
to be in each specific market. Even if a market turns out to be too costly to trade
in the end, the results derived from researching that market still help us form an
opinion on how robust the system is when traded on other markets.
For example, if a system that tries to pick small short-term profits seems to
be working equally as well in two markets, but one of the markets is very expensive to trade when it comes to commission costs, the results from that market,
when the system is tested without slippage and commission, still help us get a feel
for how good the system is at finding the moves in any market. Had we performed
the testing with slippage and commissions, the poor results from the too-expensive-to-trade market might have discouraged us from trading the profitable one.
Further, considering commissions at this point will also result in suboptimal
parameter settings for the variables in the system. Generally, considering these
costs will favor systems with fewer or longer trades, the results are therefore
skewed in those directions, and we might end up missing a bunch of good shorter-term trading opportunities.
For example, if you’re building a short-term system for the stock market, it
can be tricky to even come up with something that beats a simple buy-and-hold
strategy. But with a buy-and-hold strategy, you are in the market 100 percent of the
time, with the same amount of shares or contracts for the entire period. What if
13
you could come up with a system that only kept you in the market 50 percent of
the time, while the profit per share traded only decreased 40 percent? To assume
the same effective risk as in the buy-and-hold system, you now can trade twice as
many contracts per time units spent in the market. But with only a 40 percent drop
in return per contract traded, the final net outcome measured in dollars will still be
20 percent higher than it would have been for the buy-and-hold strategy.
For example, say that investing in 100 shares in a buy-and-hold strategy
resulted in a profit of $100. Then, trading 200 shares at the time, being in a trade
only 50 percent of the time, would result in a profit of $120 [100 * 2 * (1 0.4)].
Hopefully, the final risk–reward relationship will be even better than that,
because the whole point of a trading system, as compared to buy-and-hold, is that
the system will keep you out of the market in bad and highly volatile times, when
the result of the buy-and-hold strategy will fluctuate widely. Furthermore, with a
trading system, you have the opportunity to reinvest previous winnings to speed up
the equity growth even further, which you cannot do with a buy-and-hold strategy.
Remember that during the testing procedure, we’re only interested in how
well the system captures the moves we’re interested in and how likely it is that it
will continue to do so in the future. We are not interested in how much money it
could have made us, whether we could have traded without any additional costs or
not. Many times the value of these costs also will vary relative to the value of the
market and the amount invested in the trade, which also is something most systemtesting software cannot deal with.
For example, in a trending market, the commission settings will have a larger impact on your bottom line the lower the value of the market. We already
touched on how the dollar value of the moves is likely to increase with the value
of the market. Subtracting the same cost for slippage and commission across all
trades in such a market will only lower the impact of the low-value trades even further. The same goes for comparing different-priced markets with each other.
To test a trade, first calculate the expected percentage move you are likely to
catch, then transform that move into dollar terms in today’s market by multiplying
the percentage move by today’s market value and the number of shares to trade.
Then deduct the proper amount for slippage and commission. If this dollar value
still looks good, you should take the trade.
CHAPTER
2
Calculating Profit
A
lthough we haven’t discussed it explicitly, by now it shouldn’t be too hard to
understand why net profit is not a good optimization measure to judge a system
by. Remember, a profitable system doesn’t necessarily have to be a good system,
no matter how high its net profit. It’s all a question of which market you apply the
good system on and how aggressively you trade it.
But to clarify things a little further, let’s start out with a little analogy. Imagine
a downhill skier on his way down the slope to the finish line. About half-way down
the slope, there’s an interim time control. Let’s say the skier passes that control after
one minute, eight seconds. If the interim time control is one mile down the slope,
then the skier has kept an average speed of 53 miles per hour. Now, although we
need the interim time to calculate the average speed, it is not the interim time that
gives the average speed; it is the average speed that gives the interim time.
Compare the above reasoning with the statistics of two trading systems that
you have tested over the last 10 years. Halfway through the testing period, both
systems show a net profit of $100,000. The only difference is that one system
made that money in 250 trades, while the other one made it in 500 trades, for an
average profit per trade of $400 and $200, respectively. Which one would you
rather trade, knowing nothing else about these systems? I don’t know about you,
but I would go with the one that made the most money the fastest, with the speed
in this case measured in trades instead of hours or days. That is, everything else
aside, I would go with the system with the highest average profit per trade. At the
very end of the testing period, the same reasoning applies, because even though
you have reached the end of the testing period, it is still only an interim point in
your life and career as a trader.
15
16
Thus, since it is the speed that is behind the final result, and not the other way
around, why not aim for the source directly? Obviously, plenty of other factors
influence which system to trade, but we will get to those in a little while. For one
thing, the average profit per trade, looked at all by itself, says nothing about how
reliable the system is and how likely it is that it will continue to perform well in
the future.
Even so, a couple of other reasons exist for why the net profit should be
avoided when evaluating a trading system, no matter how rigorous the testing has
been and how robust the system seems to be. For example, the total net profit tells
you nothing about when your profits occurred and how large they were in relation
to each other. This is especially important if the markets you’re comparing are
prone to trending.
If you’ve tested the system with a fixed amount of shares for each trade, it is
likely that the dollar value of each trade has increased with the increasing dollar value
of the market. This, in turn, means that the profits are unevenly distributed through
time, and the net profit is mostly influenced by the very latest market action. In a
downtrend, the opposite holds true. Notice, however, that the trend of the market says
nothing about whether the system has become more robust or not. In a market with
several distinctive up and down trends, this matter becomes even more complex.
In a portfolio of markets, the total net profit tells you nothing about how well
diversified your portfolio is. This is especially true if you stick to trading a fixed
amount of shares for all stocks, because what is considered a huge dollar move in
some stocks or markets is only considered a ripple on the surface in others.
AVERAGE PROFIT PER TRADE
Knowing nothing else about the different characteristics of three different systems,
which one would you rather trade? One that shows an average profit per trade of
$290 over 101 trades; one that shows an average profit of $276; or one with an
average profit of $11. Assume all systems have been tested on the very same market, over the same time period, ending today, and with a fixed dollar amount
invested in each trade. All profits are measured in dollars.
I take it most of you answered the first system, with an average profit of $290.
But what if I told you that the first system also produced a distribution of trades like
in Figure 2.1? Would this system still be your first choice after you’ve compared
Figures 2.1 to 2.3? If not, which one would you have picked this time? Why?
If you said that System 1 (Figure 2.1) is not a good alternative because it’s
obvious that the trades these days are way below the value for the average trade
over the entire period, you’re on the right track—sort of. But if you also said that
System 2 (Figure 2.2) is the best alternative because it’s equally as obvious that the
average trade for that system is way below what can be expected, as judged from
the last few trades, you’re still not right enough to justify real-life trading.
CHAPTER 2
Calculating Profit
FIGURE
17
2.1
System 1 distribution of trades and profits.
Given the assumptions, there is only one reason why the distribution of
trades can look as it does in Figure 2.2: System 2 has become more and more profitable over time, which could be a very dangerous situation, because the system
might be optimized too hard to the most recent market conditions.
Personally, having seen Figures 2.2 to 2.3, and knowing nothing else about
the systems, I would go with the last alternative (Figure 2.3), because the similarities of the trades over the entire time period indicate that it has worked equally as
well all the time, which the other two obviously have not.
A system that has worked equally as well all the time will also have its
parameters set in such a way that each trade influences the final parameter settings to an equal degree as all the other trades, no matter the underlying market conditions, such as the direction of the trend. A system in which
performance has fluctuated over time (increased or decreased) will have its
parameters set in such a way that the trades from the most profitable period
have influenced the final parameter settings more than the trades from the less
profitable period.
In the case of the three systems above, this means that Systems 1 and 2 are
more likely to start to underperform (which might already be the case with System
1), and even cease to work completely, when market conditions change.
18
FIGURE
2.2
Now, pretend the columns in Figures 2.1 to 2.3 represent percentage
moves (never mind the scale on the y-axis) on a one-share (one-contract) basis.
Which system version would you go with, assuming you know nothing else
about the systems? Again, your answer should have been System 3 (Figure
2.3). Again, it’s because it’s the only system that works equally as well all the
time, no matter the trend or the quality of the different market conditions.
Because the outcomes from all the trades are very similar, it’s the only system
that gives all the trades the same weighting in deciding the parameter settings
of the system.
The other systems will give more weight to the earliest trades (Figure 2.1) or
the latest trades (Figure 2.2). This is especially dangerous in Figure 2.2, because if
market conditions change back to what they were at the beginning of the test period, the system will start to produce significantly less profitable trades, and you
won’t know why until it’s too late. A system like that represented by Figure 2.1
might, on the other hand, surprise you positively by starting to produce trades significantly more profitable than what you expected. But who in his right mind
wants to trade a lousy system only on the assumption that it is more likely to surprise you in a positive way than a negative way? What if it doesn’t surprise you at
all and just continues to be plain lousy?
CHAPTER 2
Calculating Profit
FIGURE
19
2.3
Now, say you plan to trade System 3 (Figure 2.3). Using the equal-dollar
position method, you might have decided to always tie up $100,000 in each trade
to catch a 2-percent move (on average) in every stock you’re interested in. If, for
example, a stock is priced at $50, a 2-percent move on a one-share basis will be
worth $1. Tying up $100,000 in a $50 stock means you can buy 2,000 shares, for
a total estimated profit of $2,000 (50 * 0.02 * 2,000), which also is 2 percent of
$100,000 (2,000 / 100,000).
Using the one-share percentage method, the average profit per trade in the
future will equal the average percentage move the system is expected to catch,
multiplied by the current stock price of each specific stock, multiplied by the
number of shares invested in each specific trade. For example, if the average profit per trade is expected to be 2 percent per share, the price of the stock is $100, and
you plan to buy 1,000 shares, the expected profit will come out to $2,000 per trade
(100 * 0.02 *1,000). Buying 1,000 shares of a $100 stock also means that you will
tie up $100,000, for a total percentage profit of 2 percent of the invested amount.
Note that in the first case, your plan is to tie up a certain dollar amount; in
the second example, it is to buy a fixed amount of shares. In real trading, none of
these methods are the preferred ways to go. Instead, you should always try to risk
the same percentage amount of your equity, which will alter both the number of
20
shares bought and the dollar amount invested with the changes in the equity. Only
then will your profits per trade grow, as shown in Figure 2.2, no matter the current
trend or market conditions. The discussion for why that is will have to wait until
we get to Part 4. To get to this stage, you first need to test your system so that it
trades equally as well, on average, at all times on a one-share basis, with the profits and losses measured in percentage terms, which is what we’re discussing now.
We want to measure the system’s performance in percentages, because as the
dollar value of the market changes, so will the dollar values of its moves. Thus, the
move in relation to the current market value will stay approximately the same. This
means that a low-priced market is more likely to produce small dollar moves than
a high-priced market, and vice versa. If you test a system on a low-priced market
for an average profit of $1 per share, produced by an average move of 2 percent,
the average profit in a higher-priced market will not be $1 per share, but 0.02 times
whatever the market value of that market (everything else held equal and provided the system is considered robust and stable in the first place).
Had you not known that the average profit per share traded was higher than
what your testing showed you, you might have discarded the system as not good
enough. Worse yet, reverse the logic and you might have traded a system that you
thought had a high average profit per trade when in fact it had not. Thus, the single most important thing to think about when building and examining a trading
system is to do it in such a way that you can estimate what the profits and losses
are likely to be at today’s market value (or at any other point in the future), not
what you could have made in the past. Only then can you make your results forward looking and, for example, calculate how many trades it should take you to
make a certain amount of money or trade your way out of a drawdown, as this
example will show you:
If you know that your average profit per trade, given the current market values
of the markets you’re trading and the number of shares you trade in each market,
equals $500, and you currently are in a $7,200 drawdown, the estimated number of
trades to get you out of the drawdown will be 15 [Integer(7,200 / 500) 1].
AVERAGE WINNERS AND LOSERS
Note that a 2-percent move doesn’t seem to be that much ($2 for a $100 stock and
$1 for a $50 stock), but for now, we’re talking on average over all trades, counting
both winners and losers. The average winner might be larger, say 4 percent, but
since we’re bound to a have a few losers as well, the average profit for all trades
might not be any larger than this.
Say you have a system with a stop loss of 1 percent and a profit target of
4 percent. This system is going into each trade with an estimated risk–reward
relationship of 4:1. However, because not all trades will be winners and fewer still
will be stopped out with a maximum profit of 4 percent, the actual risk–reward
CHAPTER 2
Calculating Profit
21
relationship over a few trades will be lower. To calculate the exact relationship we
need to know exactly how many losers are likely for every winner; if those numbers are missing, we can estimate the number of winners and losers based on the
system’s characteristics and our experience.
Given the current volatility of the stock market, it’s fair to assume that a
1-percent stop loss is quite tight, which should result in a rather large amount of
losing trades. Assuming that only every third trade will be a winning trade, and
that the average loser is equal to the stop-loss level of 1 percent, we can calculate
the value of the average winner according to the following formula:
AW (AT * NT AL * NL) / NW
Where:
AW Value of average winner
AT Value of average trade
AL Value of average loser
NT Number of trades
NL Number of losers
NW Number of winners
In the above $7,200-drawdown example, we assumed the average trade to be
worth $500 in today’s market. Assume further that we are currently tying up
$100,000 per trade, which then makes the average profit equal to 0.5 percent of
both the tied-up capital and the expected move of the stock on a one-share basis.
With three trades, of which one is a winner and two are losers, and the value of the
average trade being 0.5 percent, the average winner comes out to 3.5 percent [(0.5
* 3 1 * 2) / 1]. The actual risk–reward relationship is then 3.5:1.
With this information at hand, we can calculate how many winners in a row
we need to take us out of a drawdown. Continuing on the $7,200-drawdown example, it will take you three winning trades in a row to reach a new equity high if our
average winning trade is worth $3,500 [Integer(7,200 / 3,500) 1].
Now, three wining trades in a row doesn’t seem to be too hard to produce, but
because we know that only every third trade on average will be a winner, ask yourself how likely it is for this to happen. Provided it’s highly unlikely that two or
more winners will occur in a row, but very likely that the losers will come in pairs
and that your average loser is for $1,000, then you know it can be expected to take
at least 10 trades before you can see the sky again, provided you start out with a
winning trade. If you instead start out with two losing trades, taking the drawdown
down to $9,200, everything else held equal, the estimated number of trades would
be 15.
Doing the same math, but on the assumption that as many as 50 percent of
all trades will be winners, the average winner will be 2 percent [(0.5 * 2 1 * 1)
22
/ 1], for a risk–reward relationship of 2:1. If the average winning trade is worth
$2,000, the number of winning trades needed to take you out of a drawdown will
be four [Integer(7,200 / 2,000) 1]. Now, how many trades will it take to get out
of a $7,200 drawdown, assuming every other trade will be a winner and every
other trade will be a loser? It will take 13 trades, provided the first trade is a winner, but 16 trades, provided the first trade is a loser.
Obviously, you should try to keep the number of winners as high as possible
to feel comfortable with the system, but sometimes it could be a good thing to
keep this number down in favor of a higher number of profitable months for the
overall system or portfolio. Nonetheless, with these numbers at hand, we now can
put together a more generic formula to calculate the estimated number of trades,
N, to get out of a drawdown:
N Integer[DDA / (X * AW (1 X) * AL)] 1
Where:
DDA Drawdown amount
X Likelihood for winner, between zero and one
AW Average winner
AL Average loser, absolute value
For example, if the average winning trade is worth $3,500, the average losing trade $1,000, and the likelihood for a winner is 33 percent, then the estimated
number of trades to take you out of a $7,200 drawdown is 15 [Integer(7,200 / (0.33
* 3,500 0.67 * 1,000)) 1]. If the average winner is worth $2,000, and the likelihood for a winner is 50 percent, the estimated number of trades will also be 15
[Integer(7,200 / (0.5 * 2,000 0.5 * 1,000)) 1]. (More about the likelihood for
a certain amount of winners and losers is in Chapter 4: “Risk.”)
STANDARD DEVIATION
Picture yourself as a quality controller standing at the end of an assembly line.
Your pay (final estimated profit) for this job depends on how many units (number
of trades) you and your machine (system) can produce, but also on the individual
value of those units. However, because it takes the machine longer to produce a
high-value unit, which also breaks much easier than a unit of lesser value does, it
doesn’t always pay to produce high-value units. In fact, the best payoff comes from
producing nothing but average units; therefore, you’re doing your best to get rid of
Although I actually took plenty of statistics courses during my university years, I would not have been able
to write about all the statistics in this chapter without sneaking a peek at David M. Lanes’ eminent
statistics Web site at davidmlane.com/hyperstat/.
CHAPTER 2
Calculating Profit
23
the defective units as quickly as possible, but also not letting the high-value units
stay on the line for too long.
In short, you’re trying hard to maximize your payoff by making all of the
units deviate as little as possible from each other or from the average unit (to keep
a low standard deviation). Obviously, you would like the assembly line to run as
fast as possible, but only after you have examined one unit can the next unit be
placed on the line. Thus, the longer the time spent examining a single unit, the
lower your payoff will be.
Along comes an obviously defective unit that is bound to lower your results.
Without wasting any time, you toss it in the garbage, freeing up the line for another unit. The next unit looks pretty average, but to be sure, you examine it for a
while longer than you did the previous one before you take it off the line. In fact,
without knowing it, with this average unit, you spent an average amount of time.
But the third unit that comes along is much trickier. This one shows all the
right features for being a real money maker, and while you’re watching it, these
features grow even bigger, promising to make this unit at least three times as valuable as the average unit. What to do? Should you let it grow even bigger, or should
you free up the line for more units? But then, all of a sudden it breaks. You freeze
in panic, and more time passes before you come to your senses and throw it in the
garbage. In the end, the time you spent processing this too-good-to-be-true unit
could have been used processing three average units.
What happened here? By trying to increase your profits from an individual
unit, you put yourself in unfamiliar territory, which made you act in panic, thus
increasing the standard deviation of the outcome and lowering the number of units
produced. In the end, this resulted in less overall profits.
But wait a minute, you say. What about the big winners? Doesn’t the old
adage say that I should let my profits run? Yes, it does, but there is a price to pay
in doing so. The price is that you will lose track of what is average. The really big
winners are usually few and far between; the rest are just a bunch of lookalikes that
confuse you. By staying away from all of them, you are freeing both your time and
money to produce several average units, which in the end should prove both more
profitable and less risky. At the very least, you need to keep track of what is average and what is not.
This is where descriptive statistics and terms such as standard deviation,
kurtosis, and skew come in. A system’s standard deviation of returns tells you how
much an individual trade is likely to deviate from the average trade, or rather, the
likelihood that it will stay within certain boundaries, as indicated by the standard
deviation interval.
For this to be true, we need to assume that all trades are normally distributed
around their mean and that the outcome of one trade is independent of the outcome
of the others. This isn’t necessarily always the case, but we have to assume it is,
because it will most likely cost us more to not do so, in the form of either larger
24
than necessary losses or smaller than necessary profits. The formula to calculate
the standard deviation follows:
s Sqrt[(N * Sum(Xi2) Sum(Xi)2) / N * (N 1)]
Where:
N Number of trades
Xi Result of trade Xi, for i 1 to N
If the return from a trading system is normally distributed, about 68 percent of
the individual outcomes will be within one standard deviation of the mean, and
about 95 percent will be within two standard deviations of the mean (1.96 standard
deviations to be exact). For example, if the average profit for a trading system is
$500, and the standard deviation is $700, then we can say that the profit for 68 percent of all trades falls somewhere in the interval of $200 (500 700) to $1,200
(500 700), and that the profit for 95 percent of all trades falls somewhere in the
interval of $900 (500 2 * 700) to $1,900 (500 2 * 700). If, on the other hand,
the one standard deviation boundary lies at $900, the outcome for 68 percent off all
trades falls somewhere in the interval of $400 (500 800) to $1,400 (500 900).
We can see that the wider the standard deviation boundaries, the more dispersed the trades; and the more dispersed the trades, the less sure we can be about
the outcome of each individual trade. (Note that a large percentage of all trades
falls into negative territory. It is virtually impossible to build a system that can
keep its lower one standard deviation boundary in positive territory, with the
results measured on a per-trade basis.)
If taking on risk means taking on uncertainty about an unknown future or the
outcome of a specific event, then if we can be absolutely certain about the outcome of a specific trade, no matter if we know whether it will be a winner or a
loser, we take no risk. (More about the distinction between risk and loss is in
Chapter 5: “Drawdown and Losses.”) Consequently, the less sure we are about the
outcome, the more risk we’re assuming, no matter if the outcome can be either
negative and positive.
Note that, using the formula above, the standard deviation will be smaller the
larger the denominator is in relation to the numerator, which happens with an
increasing number of trades. This is also an important reason why a system should
work on (or at least be tested on) as many markets as possible, because the more
hypothetical trades we have, the more certain we can be about the outcome of each
individual trade.
Finally, you probably have heard the old saying that the larger the profits you
want to make, the larger the risks you need to assume. This is because the standard
deviation most likely will increase with the value of the average trade. This doesn’t
always have to be the case, but most often it will. The trick, then, is to try to modify the system so that the standard deviation at least increases at a slower rate than
CHAPTER 2
Calculating Profit
25
the value of the average trade, or so that the ratio between the average trade and the
standard deviation increases and becomes as large as possible. This is called the
risk-adjusted return. The system with the highest risk-adjusted return is the safest
one to trade, given its estimated and desired average profit per trade.
For example, a system with an average profit of $500 and a standard deviation of $700 has the same risk-adjusted return as a system with an average profit
of $5,000 and a standard deviation of $7,000 (500 / 700 5,000 / 7,000 0.71).
Consequently, both give you the same bang for your buck, and neither can be considered any better than the other, with only this information at hand. A system with
an average profit of $300 and a standard deviation of $400, on the other hand, has
a risk-adjusted return of 0.75 (300 / 400), which is higher than either of the other
systems, and therefore makes it the safest one to trade. To increase the profits from
a system with a low average profit but a high risk-adjusted return, simply utilize
it on as many markets as possible to increase the number of trades and, in the end,
the net profit.
DISTRIBUTION OF TRADES
So far, when we have used several of our statistical measurements, such as the average profit and the standard deviation of the outcomes, we have assumed that all our
variables, such as the percentage profit per trade, have been normally distributed
and statistically independent, continuous random variables. The beauty of these
assumptions is that the familiar bell-shaped curve of the normal distribution is easy
to understand, and it lends itself to approximate other close to normally distributed
variables as well. Figure 2.4 shows what such a distribution can look like.
Note, however, that for a variable to be random, it does not have to be normally distributed, as Figure 2.5 shows. This chart is simply created with the help of
the random function in Excel. Figure 2.4, in turn, is created by taking a 10-period
average of the random variable in Figure 2.5. Many times, a random variable that
is an average of another random variable is distributed approximately as a normal
random variable, regardless of the distribution of the original variable. This is also
called the central limit theorem. Therefore, it is likely that the average profit per
trade from several individual markets will be normally distributed, no matter the
distribution of trades within any of the individual markets, or that the profit over
several similar time periods (say a month) will be normally distributed, although the
distribution of the trades might not.
However, a normal distribution can very well be both higher and narrower,
or lower and fatter, than that in Figure 2.4. The main thing is that it has a single
mode (one value that appears more frequently than others) and is symmetrical,
with equally as many observations on both sides of the mean. For a normally distributed variable the mean, median (the middle value, if all values are sorted from
the smallest to the largest), and mode should be the same.
Occurrences
26
FIGURE
2.4
Normal distribution curve.
For the longest time, the normal distribution has been the statistical distribution most analysts used to calculate market returns, although it has long been evident that the market does not follow a normal distribution. This can be seen in
Figure 2.6, which shows the daily percentage returns for the S&P 500 index over
the period April 1982 to October 1999. As you can see, this curve is not entirely
symmetrical, and it has much fatter tails than the normal distribution curve in
Figure 2.4.
If a distribution has a relatively peaked and narrow body and fatter tails than
a normal distribution, it is said to be leptokurtic. If the opposite holds true, it is
said to be platykurtic. To calculate the kurtosis of a variable, you can use the kurt
function in Excel. In the case of the daily distributions of returns for the S&P 500
index, the kurtosis equals 56. A positive value means that the distribution is leptokurtic, whereas a negative value means that it is platykurtic. When building a
trading system, we prefer the distribution of returns be platykurtic, so that we
make sure that the system does not stand or fall with any large outlier trades.
However, this is a double-edged sword: A positive value for the kurtosis (the
distribution is leptokurtic with a narrow body) also might indicate that we are
doing a good job in keeping most of our trades as similar as possible to the aver-
Occurrences
FIGURE
2.5
Occurrences
Random variables and distribution.
FIGURE
2.6
S&P 500—April 1982–October 1999.
27
28
age trade. If that is the case, the kurtosis should increase with the number of trades
from which we can draw any statistical conclusions, while the dispersion of these
trades stays the same. That is, the standard deviation should stay the same between
alterations of the system. If both the standard deviation and the kurtosis increase,
it could be because the new system is producing more outlier trades. (An outlier
trade is an abnormally large winner or loser that we didn’t expect to encounter,
given the characteristics of the system.)
What probably cannot be seen from Figure 2.6 is that the distribution also is
slightly skewed to the left (a negative skew), with the tail to the left of the body
stretching out further than the tail to the right. Normally, a negative skew results
in a mean smaller than the median. When building a trading system, we prefer the
returns to be positively skewed, with the tail to the right stretching out further from
the body than the tail to the left, so that we make sure that we’re cutting our losses short and letting our profits run. In that case, the value of the average trade also
will be larger than the median trade, which means that for most trades, we can
expect to make a profit similar to the median value. Every so often, however, we
will encounter a really profitable trade that increases the value of the average trade
as well. This, too, is a double-edged sword in that the final outcome now is more
dependent on a few large winners, which might or might not repeat themselves in
the future. To calculate the skewness of the distribution, you can use the skew function in Excel. In this case, the skew equals 2.01, with the average return per day
equal to 0.0296 percent and the median equal to 0.0311 percent, respectively.
STANDARD ERRORS AND TESTS
Many times, when testing a system on several markets, it is easier to work with the
averages from each system/market combination (symac) and then calculate an
average and standard deviation interval around this newly computed average of all
other averages. This presents a small statistics problem, because when we work
with averages from several samples to calculate an average of those averages and
a standard deviation interval around the new average of averages (now called the
standard error), we really should use the following formula:
sM ∑s2 / N
2̇
Where:
sM Standard error of average from all markets tested
∑s Standard deviation of all trades from all markets
N Number of markets tested
As you can see from the formula, sM will be smaller than s (how much
depends on N). Because both a single sample observation and a sample average
are estimates of the same true average for the entire population, and because there
CHAPTER 2
Calculating Profit
29
is a higher likelihood for a sample average to come close to the true population
average, the standard error for a set of sample averages will be smaller than the
standard deviation for a set of individual observations.
The problem with this formula is that, if we first calculate an average profit
per trade and market, we won’t be able to find the standard deviation of all trades
from all markets, and if we did, we wouldn’t have a need for this formula in the
first place. So, what to do, and why?
Let’s start with the why. We’re doing this because testing a system over several markets (I usually use 30 to 60 markets, tested over the last 10 years of market action) produces lot of trades, which makes things very cumbersome and
results in very large Excel spreadsheets needed for the calculations. It is also valuable to know the standard error of the average for future reference, if and when we
start to trade the system for real and would like to compare the averages it produces in real-life trading with those estimated from the testing.
Nonetheless, somehow we need to come up with a value for the standard
deviation of all trades from all markets. To do this, assume that the variable we’re
investigating isn’t the profit per trade, as in the original standard deviation formula, but the average profit per trade from several markets. Use the same formula to
compute s. In that case, N in the original formula will represent number of markets tested, and Xi the average profit from a specific market, as indicated by i. (A
more correct way would be to calculate all the averages and standard deviations
for all the markets tested and then calculate a standard error of the averages as a
function of the mean square error, which simply is the average of all standard
deviations. But what the hell—this is not a book about statistics.)
It is important to remember that whatever variable we’re investigating—such
as the average profit per trade—will always be an estimate of the true average
profit per trade. This is because no matter how many markets we’re using and how
far back in time we do the testing, the test will only contain a small sample of markets producing the price pattern the system is trying to catch. Think about it: There
are various types of markets all over the place, and some of them are already several hundred years old. It would be impossible to collect all the data to test them
to compute the true average profit per trade for a specific system, as of today. And
even if we could do that, the true value, as of today, would be nothing but an estimate for what the true value will be at some point in the future, when all markets
cease to exist.
Therefore, it would be interesting if we could calculate an estimate, or at
least some sort of a confidence interval, for what the true average profit per trade
might be. For example, what if we, using our 30 to 60 markets and 10 years of
data, calculate the average profit per trade for a system to be $300, when in fact
the true value is $100, and the system slowly but surely starts to move closer to
that value over the next several years, when we’re trading it live. In that case, the
system has not broken down and the market conditions have not changed.
30
Unbeknown to us, it’s just behaving as it always has and should. We just happened
to do our research on a set of markets and a period that wasn’t representative for
the types of results this system really produced.
Remember that a one standard deviation interval around the mean should
contain approximately 68 percent of all observations, and a two standard deviation
interval around the mean should contain approximately 95 percent of all observations. Now we can twist that reasoning around a little bit and say that we can be
95 percent sure the true average value of the variable we’re testing is between 2
standard errors around the just-computed average of averages. We do that using
the following three-step process:
First, calculate the average profit per trade for each market tested (this is the
variable we’re investigating), an average for all those averages (this is the average
to estimate the true average), and the standard deviation for those averages, using
the standard deviation formula.
Second, use the standard deviation just calculated to calculate the standard
error for all averages of averages. For example, for a standard deviation of $700
over thirty observations (markets tested), the standard error will be $128 [700 /
Sqrt(30)].
Third, multiply the standard error by 2 (for two standard errors, to produce a
95 percent confidence interval), and add and deduct the product to and from the
average profit per trade, calculated earlier as the average of several market averages. For example, with an average profit per trade of $300 and a standard error of
$128, we now can say that we can be 95 percent sure that the true (always unknown)
average profit per trade will fall somewhere in the interval $244 to $756.
Because the true standard deviation will always be unknown, the factor we’re
multiplying the standard error by actually should be slightly higher than the standard error interval for which we’re creating the confidence interval, depending on
the number of observations we’re working with (30, in this case). You can look up
the exact value in a so-called t-table in any statistics book. However, because 30
to 60 observations is considered to be a fairly high number of observations, this
number will be very close to the standard error value anyway (2.0423 for 30 observations).
OTHER STATISTICAL MEASURES
Another way to make sure that a system is not too dependent on any outliers is to
exclude them when you are calculating the average return. You can do this in Excel
with the trimmean function, which excludes a certain percentage of observations
from each end of the distribution. Ideally, when building a trading system, we prefer
the trimmean to remain above zero, so that we make sure that the bulk of our trades
behave as they should. If the trimmean is larger than the average return, it indicates
that the positive outliers are larger than the negative outliers, and vice versa.
CHAPTER 2
Calculating Profit
31
In this case, whatever you think is best depends on what you expect and how
you would like the system to perform in the future. After a few bad trades, it could
be comforting to know that the positive outliers historically have had a tendency
to be larger than the negative ones; on the other hand, having to rely on a set of
not-yet-seen outlier trades to find your way out of a drawdown seems awfully
close to desperate gambling if you ask me.
If we don’t know for sure whether the distribution is approximately normal or
not, we cannot use our normal distribution measurements, which, for example, say
that 68 percent of all observations will be within one standard deviation of the mean.
Instead, we have to use Chebychef’s theorem, which says that for a k greater than or
equal to 1 (k 1), at least (1 – 1 / k2) observations will fall within k standard deviations of their mean value. Note that with this method, we cannot give an exact value.
For example, if we have a normal distribution, we know that 95 percent of all
observations will fall within two standard deviations; but if we don’t know what
the distribution looks like, we can only say that at least 75 percent (1 1 / 22) will
fall within two standard deviations. Furthermore, without knowing the exact distribution, we cannot say if they will be equally distributed around the mean. We
have to estimate this from our kurtosis and skew measurements. Similarly, to
encapsulate at least 50 percent, 67 percent, and 90 percent of all observations, the
standard deviations must be 1.41, 1.74, and 3.16, respectively.
When we’re building a trading system, we do not want the distribution of
trades to be normally distributed, but instead to fall into a few very distinctive bins
or categories, such as a certain sized profit and a certain sized loss. Thus, we know
exactly what we can expect from one trade to the next. Figure 2.7 shows one such
distribution of trades. In fact, if you ask me, a normal distribution of trades within a specific market or time period indicates bad research and sloppy trading.
Remember that the normal distribution is a function of a random variable, and we
don’t want the outcome of our trades to be entirely left to chance, do we?
TIME IN MARKET
Many traders and analysts pay very little or no attention to the number of trades a
system is likely to generate. However, this is very important information that will
give you a first clue to whether the system is suitable for you. The questions you
need to ask yourself are, “Does this system trade often enough and does it keep me
in the market enough to satisfy my need for action?” These are seemingly silly
questions at first glance, but the truth is that a specific system will not suit everybody, no matter how profitable it is. If it doesn’t fit your personality or style of
trading, you will not feel comfortable trading it.
Even more important, however, is how much time the system is expected to
stay in the market, because time spent in the market also equals risk assumed.
Therefore, the less time you can spend in the market to reach a certain profit, the
Occurrences
32
FIGURE
2.7
Distinctive distribution of trades from successful trading systems.
better off you are. (Recall the example in the section “Net Profit,” which produced
a higher return than a buy-and-hold strategy, even though it spent less time in the
market and with a lower average profit per share traded.) To calculate the relative
time spent in the market, multiply the number of winning trades by the average
number of bars for the winners. Add this to the number of losing trades, multiplied
by the average number of bars for the losers. Finally, divide by the total number of
bars examined. Time spent in the market is a double-edged sword, because the less
time spent in the market to reach a certain profit, the longer it also might take to
get out of a drawdown.
Let’s get back to the examples about trading your way out of a drawdown presented earlier. What if the system in question produces approximately two trades
per month and market, and the average trade length is three days? If you only trade
the system on one market, the number of days in a trade to get you out of a $7,200
drawdown is 45 (15 * 3). But because the system only spends about 30 percent of
its time in a trade (6 / 20), the actual number of trading days to get back into the
black is 150 (45 / 0.3). That is more than six months’ worth of full-time trading to
CHAPTER 2
Calculating Profit
33
get out of a situation that at a first glance only looked like a situation that needed
“just a few good trades.”
This shows that trading is a very deceiving business, and that we’d better make
sure that we know what we are doing. Obviously, one thing that could speed up
things considerably is to trade the system on several markets. Using three
markets, the system will spend approximately 90 percent of its time in the market
(3 * 6 / 20) in one system or another, and the time to get out of the same drawdown
will be 50 days (45 / 0.9). To get out of a $7,200 drawdown in only three days
requires that the system is applied to a total of 50 markets [(45 / 3) * (20 / 6)]. Of
course not all of them will be traded, but that’s how many markets it takes, on average, to produce the 15 trades needed to get out of the drawdown in three days, considering how often and for how long the system is in a trade per market.
Obviously then, it becomes very important that the system works equally as
well in all markets, on average, and at all times. And how do we assure that? By
testing the system on as many markets as possible, covering as many different market conditions as possible, striving to make the system work equally as well, on
average, at all times, no matter the trend or price of any individual market. The way
to avoid fitting the system parameters to any specific market or market condition
is to measure its performance in percentage terms on a one-contract basis. Have
we stated this enough times now?
Note also that with 15 trades needed to get out of the drawdown in three days,
and with the average time per trade also being three days, we need to be in all 15
trades simultaneously. Unfortunately, however, given the initial assumptions for this
situation, being in 15 markets simultaneously is impossible for most of us.
Remember that earlier we needed to tie up $100,000 in each trade, which means that,
to be in 15 positions at one time, we need to have at least $1,500,000 on account.
But what if we only have, say $500,000, and never want to tie up more than
40 to 60 percent of that amount? Well, then we can only be in three trades at a time
(500,000 * 0.6 300,000), which means we can only apply the system to 10 markets (20 * 3 / 6). If we apply it to more markets than that, we will have to start second-guessing the validity of the signals produced by the system and exclude some
of the trades according to our own whims—something we most definitely do not
want to do. Fortunately, there is a way to ease this dilemma, which we will get to
in Parts 3 and 4. For now, however, we can only conclude that we also need to keep
numbers and equations like this in the back of our minds so that we don’t fool ourselves into trading a system that isn’t suitable for us.
Note also that, in this example, we are working with fixed dollar amounts
invested under the assumption that the market levels will stay approximately the
same. In Part 4, where we start working with dynamic amounts, depending on both
the market level and the account equity, an ever-changing number of shares will
be traded on a wide variety of both markets and systems, which makes this matter
even more complex.
CHAPTER
3
Probability and Percent of Profitable Trades
One of the most important factors to consider when researching a trading system
is its percentage of profitable trades. Counterintuitive as it might seem, a higher
percentage of profitable trades isn’t necessarily better than a lower number. It all
depends on what you’re trying to achieve with the system, and how it relates to the
average profit per trade, how often a trading opportunity presents itself, and how
long a typical trade lasts.
Together with the profit factor, the percent profitable trades is the only performance measurement that has any value when it comes to estimating the system’s future
performance that can be derived immediately from the single-market performance
summary produced by many off-the-shelf analysis programs. Again, this is assuming
the underlying logic is sound and the system can be considered robust. Normalization
should not matter. That is, for the number of profitable trades to be correct, you don’t
need to look at the results in terms of equal amounts invested or percentages.
It boils down to making sure that your system has a positive mathematical
expectancy. Make sure that the relative amount of your winning trades (or percentage winners) multiplied by the average profit from those trades is sufficiently larger than the relative amount of the losing trades (or percentage losers) multiplied by
the average loss from those trades. If this value is above zero, the system has a positive mathematical expectancy, which is a key criterion for any trading system.
CALCULATING PROFITABLE TRADES
To calculate the percentage of profitable trades, simply divide the number of winning trades by the total number of trades produced by the entry rule over the test
35
36
period. For easier interpretation, you also can multiply by 100. For example, if a
system has produced a total of 52 winners over 126 trades, the percentage profitable trades is 41.27 percent (52 * 100 / 126). From this, it follows that 58.73 percent [100 41.27, or (126 52) / 126] must be losers or break-even trades.
If the average winner and loser are worth $500 and $400, respectively, and
the historical (or back-tested) track record shows that the system has produced 45
percent profitable trades (and consequently 55 percent losers), then the mathematical expectancy for the system equals $32.5 [(0.45 * 500) (0.55 * 350)].
When looking at these numbers, it’s important to remember that a historically high percentage of profitable trades doesn’t necessarily mean an equally high
likelihood for the very next trade, or each individual trade, to be a winner. The reason for this is somewhat abstract and philosophical: As soon as any series of words
or numbers result in something that is not random, it contains information. And as
soon as there is information in anything, we can distill it from the background
noise and make it work in our favor.
In the case of a trading system, this is equal to refining the system to make
better use of the nonrandom signals the market gives us. However, the consequence is that the closer we get to distilling all the information, the closer the system comes to acting in a random manner. When we have refined the system as
much as we can, but still think we can detect some information, such as seemingly predictable runs of winners and losers, we are still better off assuming that
information is not there. This is because even a very complex and seemingly nonrandom series of data still can be the product of randomness—as for example, this
sentence (just kidding).
If we assume nonrandomness when none exists, we run the risk of trading too
aggressively when we shouldn’t, and not aggressively enough when we should,
which over time will result in a less than optimal equity growth. The best way to
avoid this dilemma is to assume randomness and to trade at an equally aggressive
level all the time. Consequently, even if you have more than 50 percent profitable
trades in your testing and historical trading, you are better off not assuming more
than that in your real-life future trading.
In fact, considering that a random entry, at best, has a 50 percent chance of
ending up with a profit (not considering slippage and commission), factoring in
these costs of trading will take the likelihood below the 50 percent level. Exactly
how much lower is hard to estimate and depends on how large these costs of trading are in relation to the profits and losses produced by the system. Therefore, if
your back testing or historical trading results show a high percentage of winners,
it could be because of two things: Either the system is good enough to overcome
the negative biases stacked against you, or the results so far (whether actual or the
product of back testing) are pure fluke.
Furthermore, assuming a 50 percent chance for the market to move a specific distance in either direction from the entry point, there still is a larger chance for
CHAPTER 3 Probability and Percent of Profitable Trades
37
a random trade to end up a loser, because of the mandatory risk–reward relationship of at least 2:1 that you should have in place when entering the trade. That is,
because you should not enter into a trade if you don’t believe that the profit potential is at least two times the value of the loss, a shorter distance between the entry
point and the loss, than between the entry point and the estimated profit, still adds
to the likelihood for the trade to become a loser.
Another reason why a high percentage of profitable trades isn’t necessarily
better than a low percentage is that a system with a low percentage of profitable
trades is more likely to continue to produce that percentage, or better, in the future:
The dollar value of the winners and losers aside, each trade only has two possible
outcomes. It can end up either as a winner or as a loser. (Break-even trades don’t
count.) With each trade only having two outcomes, a sequence of two trades must
look like any of the following four sequences: (Win, Win), (Win, Loss), (Loss,
Win), or (Loss, Loss).
And a sequence of three trades must look like any of the following eight
sequences: (Win, Win, Win), (Win, Win, Loss), (Win, Loss, Win), (Win, Loss,
Loss), (Loss, Win, Win), (Loss, Win, Loss), (Loss, Loss, Win), or (Loss, Loss,
Loss).
Thus, for every trade added to the total number of trades, the number of
sequences doubles, so that with 10 trades, the number of possible sequences is
1,024 (2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 2^10) and for 100 trades, the number of possible sequences is 1,267,650,600,228,229,401,496,703,205,376 (2^100,
or approximately 12.7 billion * 10^20), ranging from 100 winners in a row to 100
losers in a row, covering every possible sequence in between, including the one
produced by the system in question.
With that many possible outcomes, it’s easy to see that the one sequence produced by any system is nothing but a freak occurrence that is very unlikely to
repeat itself in the future, and that any system, in the future, is much more likely
to produce any other sequence of trades but the one just produced. In fact, no matter the number of trades examined, the sequence just produced—no matter how
many winners and losers it held—is no more likely to repeat itself the next time
around than the one sequence containing only winning trades.
However, even if the likelihood for the exact same sequence to occur again
is infinitesimal, a good chance still remains that the system in question will produce a sequence holding the same percentage of winners. How good depends on
how many winners we’re looking for. For example, in the three-trade sequence
above, there is only a 12.5 percent chance (1 / 8) for each sequence to happen, but
an 87.5 percent chance (7 / 8) that the sequence will hold at least one winner, and
a 50 percent chance (4 / 8) that the sequence will hold at least two winners, placed
somewhere within the sequence.
One interesting question to ask yourself when you’re examining a trading
system is how likely is it for the system to continue to produce the same percent-
38
age of winning trades? To answer that question, you need to apply the following
piece of math to your trading statistics:
P(r) [N! / (r! * (N r)!] * p^r * (1p)^(Nr)
Where:
P(r) Probability for exactly r profitable trades
N Total number of trades
r Profitable trades
p Probability for trade to be profitable
In Excel, the formula can look something like this:
(FACT($G$2)/(FACT(ROUND($B5/100*$G$2,0))*FACT($G$2ROUND($B
5/100*$G$2,0)))*(C$4/100)^ROUND($B5/100*$G$2,0)*(1C$4/100)^($G$2
ROUND($B5/100*$G$2,0)))*100
Where:
Cell G2 Total number of trades
Cell B5 Profitable trades
Cell C4 Probability for trade to be profitable
Figure 3.1 shows how this formula can be used to create a matrix, with the
data in the matrix indicating the likelihood for a specific amount of profitable
trades, given the historical profitability and your estimate of how likely it is for
each trade to be profitable in the future. Using the data in the matrix, you also can
produce a chart like that in Figure 3.2, which shows the same thing in a graphic
way. Looking at Figure 3.2 we can, for example, see that if the historical profitability is 60 percent, and you estimate the likelihood for a future trade to be a
winner at 50 percent, there is only a 1 percent likelihood that the number of profitable trades will be 60 percent over a large number of trades.
Figure 3.3 shows the cumulative likelihoods for a certain percentage amount
of trades to be profitable in the future. For example, with a 60 percent historical
profitability, and the likelihood for a future trade to be profitable at 50 percent, an
almost 100 percent likelihood exists that a longer series of future trades will hold
50 percent or less profitable trades.
The point is that no matter the percentage of profitable trades you had in the
past, the likelihood to repeat that exact amount in the future is very small—not to
mention the likelihood for producing a series of trades with the winners and losers in the same order as the historical or back-tested series.
The same goes for the number of winners and losers in a row. If for nothing
else, you should try to keep these numbers as low as possible (especially the losers, if you like to feel comfortable with trading the system). However, for a cor-
FIGURE
3.1
Matrix indicating likelihood of profitable trades.
FIGURE
3.2
Chart indicating likelihood of profitable trades.
39
40
FIGURE
3.3
Cumulative likelihood of winners and losers.
rectly built system, with a relatively high amount of profitable trades, these numbers hold very little value and should be looked upon more as freak occurrences
than anything else. Losing streaks will happen even for the most correctly built
system, and sometimes it is good to have many losing trades in a row during the
back testing, because the more losing trades in a row you’ve just experienced (for
real or during back testing), the less likely it is you will go through the same experience again, provided you’ve done everything else correctly, the logic behind the
system makes sense, and all other system statistics are reliable.
To calculate the likelihood for a certain amount of winning or losing trades in
a row, given a certain amount of trades, you can use the following formula in Excel:
MIN(MAX(0.5^(C$32)*($B4(C$32)1),0),1)
Where:
Cell C3 Winners or losers in a row
Cell B4 Total number of trades
Figure 3.4 shows how this formula can be used to create a matrix, with the
data in the matrix indicating the likelihood for a specific amount of winners or los-
FIGURE
41
3.4
Matrix indicating likelihood of winners and losers.
ers in a row, given a certain amount of trades. Note that we always need two trades
or more for the total number of trades to be able to calculate an exact amount of
winners and losers in a row.
For example, to calculate the likelihood to experience exactly two losers in a
row, we need one winner to begin the sequence, then the two losers, and finally
one more winner to put an end to the losing streak. This makes the trading
sequence look like: (Win, Loss, Loss, Win). With a total of four trades, only one
of the 16 possible sequences can look like this, which makes the likelihood for that
particular sequence to happen equal to 6.25 percent (1 / 16). (See cell C7 in Figure
3.4.) With a total of five trades, four sequences are possible having two losers in a
row, either (Win, Loss, Loss, Win, Win or Loss) or (Win or Loss, Win, Loss, Loss,
Win), which makes the likelihood for any of them to come true equal to 12.5 percent (4 / 32). (See cell D8 in Figure 3.4.)
Using the data in the matrix, you also can produce a chart like that in Figure
3.5, which shows the same thing in a graphic way. Here, we can see that the likelihood of experiencing as many as 15 losing trades in a row is very small for a total
number of trades ranging from 50 to 100. Now, that is not to say that it can’t happen, but the likelihood for it is very small. If you already have experienced such a
losing streak, either for real or during back testing, the likelihood for it to happen
again within a 100-trade trading sequence is minuscule.
In fact, exactly how large the chance is, is depicted in Figure 3.6, which
shows the likelihood for a few different trading scenarios, given a trading sequence
of 100 trades. The line in the middle shows the likelihood to experience exactly a
certain number of winners or losers in a row. The rightmost line shows the likeli-
FIGURE
3.5
Percent likelihood
Chart indicating likelihood of winners and losers.
FIGURE
3.6
Relative likelihood of winners and losers.
42
43
hood to experience a streak of at least a certain number of winners or losers. For
example, the likelihood to experience at least nine winners or losers in a row is just
below 10 percent. The leftmost line shows the likelihood to experience two trading sequences of the same length within 100 trades. For example, for five winners
or losers in a row, the likelihood to experience two such sequences is below 50 percent, and to experience two sequences of nine winners or losers in a row, the likelihood is almost 0 percent.
Note, however, that all this assumes that you’ve done everything correctly,
the logic behind the system makes sense, and all other system statistics are reliable. Also, this statistic works both ways: If you just experienced a large number
of winners in a row, it doesn’t mean that the system has gotten much better and
will continue to produce the same type of winning streaks in the future. Quite the
contrary: Depending on the size of the winning streak, the more difficult it will be
to repeat it. It’s all a game of statistics. Nothing else.
THE DIFFERENCE BETWEEN TRADES AND SIGNALS
During the initial testing of a system, we really shouldn’t concern ourselves with
the performance of the system, but rather the reliability of the signals it generates.
To do that, we really need to test all the signals generated, using standardized stops
and exits—such as, always exit after a specific profit or loss or after a specific
number of bars in trade.
Normal system testing usually only tests the first signal in a cluster of entry
signals and assumes that the others can be ignored because you would have been in
a trade already. However, whether you would have been in a trade or not depends
on your stop-loss and profit-taking levels and how long the trade should last if none
of these levels is hit. Plenty of other reasons could exist for why the first signal
might have been ignored in real-life trading, such as already being fully invested
because of previous trades, or simply because you missed trading that day.
Therefore, when researching a system, it’s important to look at all the signals
it generates, so that it can be trusted just as much on its second or third signals as
it can on its first signal. For example, assume you missed a signal one day because
of a doctor’s appointment. The next day, you get a new signal in the same stock,
despite the fact that you should have been in this stock already had you been able
to trade the previous day. If you haven’t done your research properly, you have no
idea whether the second signal is likely to be as valid and reliable as the first one.
On a more hypothetical note, there also are plenty of days when the system
just barely manages to produce a signal, or conversely, just barely misses producing a signal. (Should the near misses perhaps be as valid as the near hits? We won’t
answer that particular question here, but it’s still worth asking.) Look at Figure 3.7,
which shows a chart of all the signals that one of the systems featured in Part 2
generated in Microsoft during the fall of 2001. It shows that in early August 2001,
44
FIGURE
3.7
Microsoft performance signals—Fall 2001.
two signals went short only one day apart from each other. In late October and
early November, two signals two days in a row went long. In the case of the short
signals, clearly the second signal was better than the first signal. In the case of the
long signals, the first signal was better. However, the point is that in either case,
the second signal most likely would have gone unnoticed and unanalyzed, because
you already would have been in a trade generated by the first signal.
Now, pretend that a few of the signals that came first in a row of two or more
signals really didn’t happen, or that you for one reason or another failed to act on
them. Then you would have had to rely on the second signal. Transfer this reasoning to a real-life trading situation. How many days have you had when you saw a
nice setup forming and readied yourself to place the trade if the stock in question
only reached a certain level? Have they all resulted in a trade? Probably not. The
next day, the stock takes off in the anticipated direction, leaving you behind until
late in the day, when you actually get the signal you were looking for yesterday.
With the market already having made a good move in the anticipated direction, do
45
you trust your system enough to take the trade this time? Only a complete test of
all signals will give you that confidence.
The same reasoning holds for the exit techniques as well. To make the most
out of the chart pattern and the exit techniques that should go with it, you need to
have done your homework before you set out to trade the pattern in question and
analyze the exits in such a way so that they work, on average, equally as well for
all signals, no matter whether each particular signal would have been traded or not.
Therefore, the testing must be done in such a way that all signals will be tested at
one time or another together with several different exit levels. To do this, trade the
system at random several times.
To accomplish this, a random number generator that produces either a 0 or a
1 will be attached to the entry rules (see the TradeStation code in Chapter 7), so
that the system only can enter when the random number is 1. For example, if the
random number for the entry had been 0 for the late-October long-entry signal in
Microsoft, that trade would not have been taken; this would have made it possible
for the system to enter on the following day. Otherwise, this would not have happened, because we would have been in a trade already, which would have left the
FIGURE
3.8
Microsoft trading using RNG.
46
second signal unanalyzed. (To learn more about this system and its trailing stop
version, see Active Trader magazine, February 2002 to June 2002.)
Once the system and all its signals is fully tested, the random number generator can be turned off, so that the system can be tested according to normal principles. Figure 3.8 shows a few sample trades in Microsoft, using the original
model with the random number generator (RNG) set on. Compare these trades
with the signals in Figure 3.7 and you will find that the RNG prevents you from
taking all signals generated by the system, which means that the RNG version of
the system will not always trade the first signal in a series of signals.
As discussed more thoroughly in Part 3, one way to alter the system’s characteristics is to vary the stops and exits. Figure 3.9 also shows a few trades generated with
the RNG set on, but also with a different set of exits than those used for Figure 3.8. In
the case of Figure 3.9, the stops and exits are much tighter than those for Figure 3.8,
which makes the system trade more frequently. Compare the trades with those in Figure
3.8 and the signals in Figure 3.7, and you will see that they are different. However, note
also that another reason for the differences between Figures 3.8 and 3.9 is that the RNG
is on in both cases; it therefore generates the trades in a random manner.
FIGURE
3.9
Microsoft trading RNG, but different exits.
46
CHAPTER
4
Risk
I
once stumbled upon an Internet site dedicated to systems trading and design. The
site presented a mailing list, with various postings from systems traders asking for
and giving each other advice on various topics regarding this intricate subject. As
I was sitting there skimming through the messages, a new message came in from
a guy who asked all the other traders frequenting the site to join forces with him
to build a truly professional system—a system unlike the ridiculous systems they
all were trading right now, with back-tested profit factors (the gross profit divided by the gross loss) ranging from about two to four. Together, they should be
clever enough, he reasoned, to come up with a system that had a profit factor of at
least seven—just like the professionals.
I am sorry to say that this guy has it all wrong. There probably is no such
thing as a trading system with a back-tested profit factor of seven that has continued to stay profitable at all in real-life trading, and there most definitely is no professional money manager trading such a system. A professional and successful
money manager knows better than to fall into that trap, which unfortunately can’t
be said about many of the system vendors hawking their stuff to guys like the one
who posted the message.
In fact, many system vendors and so-called trading experts don’t want you to
trade a system with a back-tested profit factor below three (the higher the better,
they reason), because they know from experience with their own systems that the
profit factor will decrease considerably when the system is traded live on unseen
data. The only reason for this recommendation is that they do not understand how
to build a robust trading strategy in the first place, which becomes painfully evident when they continue to use the total net profit and drawdowns as their most
important performance evaluators.
47
48
The same goes for the message-posting guy. He probably has a bunch of trading systems with back-tested profit factors around four, none of which come anywhere close to showing the same profitability in real life—chances are he’s even
losing money. The solution, he believes, is to crank up the back-tested profit factor to
around seven and hope that he will land somewhere around three or four in real life.
Two related objections against that type of reasoning need to be raised here.
Number one is the robustness of a profit factor as high as seven, or even three.
Number two is the absurdity of it in the first place. Let’s start with the absurdity,
which also will help us understand why such a high profit factor is more likely to
ruin you than anything else.
Building a good and robust trading system is not a question of maximizing
the profit factor, but simply making it as reliable as possible and just high enough
to warrant trading at all. It should be high enough so that the return on the amount
risked is higher than what you could have made elsewhere, plus an appropriate
premium for assuming that risk. Think about it as any normal fairly long-term
business endeavor. What is the most you expect to make on the amount risked
when opening up a coffee shop, a dental practice, a small factory producing plastic thingies, on investing (not trading) in the stock market? Probably not more than
25 percent a year, and the stock market has an average long-term return of around
12 percent. Then what makes you think you can make so much more trading? Do
you have any idea what type of returns on the amount risked that a profit factor of
two, three, or seven represents? If not, I will tell you.
CALCULATING RISK
To calculate the profit factor, simply divide the gross profit by the gross loss. The
answer will tell you how many dollars you are likely to win for every dollar you
lose. For example, say that you have $2 and decide to take part in a game where
you have a 50 percent chance to win and, every time you do so, you win twice the
amount you risked. The first time you try, you risk $1. You lose, and your gross
loss is therefore $1. With your last dollar, you take another chance and this time
you win $2, ending up with a total of $3, and your gross profit is therefore $2. Two
divided by one equals two, which is your profit factor.
Now assume that the game changes so that you only have a 33 percent chance
to win, but when you win, you win three times the amount you risked. This time,
you start out with two losing bets, and your gross loss, therefore, is $2. With your
last dollar, you win $3 and end up with $4. In this case, the profit factor comes out
to 1.5 (3 / 2). (If you look at all five trades, you lost three trades for a total of $3
and won two trades for a total of $5, for a total profit factor of 1.67 [5 / 3].)
The profit factor tells you how much money you made in relation to how
much money you lost. How much money you lost and how much money you actually risked is not the same thing. The amount risked is equal to the total amount
CHAPTER 4
Risk
49
you are willing to lose in each and every trade, for the possibility of making a profit, just as you’re willing to risk a certain amount to get a 25 percent yearly return
on your dental practice.
Given the above numbers, it also is possible to calculate how much money
you risked. In the first example, you made a total of two bets for $1 each, which
means you risked $2 to increase your capital with $1. Consequently, your return
on the amount risked was 50 percent (1 / 2). In the second example, your capital
also increased with $1, but this time you had to risk $3, which resulted in a 33 percent (1 / 3) return on the amount risked. In total, you risked $5 to make $2 for a
return of 40 percent on the amount risked.
Now, instead of talking about a few individual bets, let’s compare each example with a year’s worth of trading, risking $1,000 in each trade. For the first year
100 losers and 100 winners produce a profit factor of two [(100 * 2,000) / (100 *
1,000)], and the return on the amount risked is 50 percent [(100 * 2,000 100 *
1,000) / (200 * 1,000)]. For the second year, with 200 losers and 100 winners, the
profit factor and the return on the risked amount will be 1.5 and 33 percent,
respectively. (And for the two years combined, the profit factor and the return stay
at 1.67 and 40 percent, respectively.)
Now, assuming a profit factor of seven for each year, let’s try to calculate
backwards to find out how large the winners need to be and what the return on the
risked amounts will be, given that we have 50 percent profitable trades in year one
and 33 percent profitable trades in year two. For year one, it’s easy enough. The
winners need to be worth $7,000, so that the calculation for the profit factor will
look as follows: (100 * 7,000) / (100 * 1,000). If that is the case, the return on the
amount risked will be 300 percent [(100 * 7,000 100 * 1,000) / (200 * 1,000)
6 / 2]. For year two, to end up with a profit factor of seven, each profitable trade
needs to be worth $14,000, so that a profit factor of seven can be calculated
according to: 100 * 14,000 / 200 * 1,000. The return on the risked amount will
then be 400 percent [(100 * 14,000 200 * 1,000) / (300 * 1,000) 12 / 3].
Now, I’m asking you, when was the last time you saw a trader (professional
or otherwise) produce a long-term sustainable return on total amount risked of 300
to 400 percent a year? Heck, when was the last time you saw any trader produce a
long-term sustainable return of 40 percent (a profit factor of 1.67, with 40 percent
profitable trades)? Never, I say. A return of 40 percent a year simply isn’t sustainable in the long run, much less a return of 300 to 400 percent. Sure, every so often
a lucky few manage to produce spectacular numbers over a year or two, but that is
only because everything goes their way during that period, with a trading strategy
or system using a long-term profit factor that could be as low as 1.25.
If it really was feasible for a professional money manager to trade long-term
with a profit factor of seven, it would be a piece of cake for someone like me, who
has dabbled around with this for ages, to come up with a system with a profit factor of at least four and more than double my money every year. But I still make the
50
bulk of my money analyzing the markets, rather than trading them. And you, I
assume, would not have bought this book if you already were doubling your
money every year. Go figure.
Remember how earlier we calculated the risk–reward relationship for each
individual trade to be 2:1 and 3.5:1, using a system with 50 percent and 33 percent
profitable trades, respectively? Can we agree that those numbers are pretty much
what any trader could ask for, professional or not? (The chart with its support and
resistance levels doesn’t look any different for you than for the professional money
manager.) Well, in the above examples, with a profit factor of seven, these
risk–reward relationships come out to 7:1 and 14:1, respectively. Where on Earth
would those moves come from, when all we can agree to is that 3.5:1 is as good
as it will ever get on a long-term, sustainable basis?
Nevertheless, say that you happen to have a system with a profit factor of
seven, a risk–reward relationship of 7:1 and 50 percent profitable trades. What
would happen if the market, unbeknown to you, changed its characteristics ever so
slightly so that you would be better off with a $2,000 stop loss instead, and that it
would be better with a profit target at $6,000, for a risk–reward relationship of 3:1
(6,000 / 2,000)? More trades would be stopped out with a $1,000 loss, and fewer
would be stopped out with a $7,000 profit. Say that every other would-be $7,000
winner now turns into a $1,000 loser, and most of the remaining winners are
stopped out for inactivity at $4,000. In that case, you’re down to 25 percent profitable trades and a profit factor of 1.33 (4,000 / 3,000). Now, with such a high percentage of losing trades, you won’t always experience one winner for every three
losers. What if you have nine losing trades in a row? Then you need at least three
winners to take you out of the drawdown, and with only a 25 percent likelihood of
each trade being a winner, chances for that to happen aren’t very high. All of a
sudden your Holy Grail system has turned into something very nerve-racking to
deal with, with drawdowns that most likely will force you out of business, even
though it still has a profit factor as high as 1.33.
What I’m trying to say is that such a highly specialized machine as a trading
system with a profit factor of seven will break apart very easily. And when one
part goes, the real trouble starts. Even though it still might be profitable, the
plunge in the profit factor will be deep, and it will be very nerve-racking to trade.
And what if the relationship between that very complex pattern or indicator setup
demanded for such a system, and the move that follows it, cease to exist completely? Compare such a system to the cheetah we talked about in the Introduction:
You will have one dead trading system, or one that produces nothing but losers.
If you ask me, any system with a back-tested profit factor of more than two
is suspect. To build a robust trading system that is likely to continue to perform
well in the future, make sure that the underlying logic is sound and simple, that the
trading rules are as simple and as few as possible, that it works just as well for a
wide range of parameter settings, that it produces plenty of trades at all times, and
CHAPTER 4
Risk
51
that it works equally as well in all markets and market conditions. If you manage
to do all this, you will be surprised at how much you can expect to produce from
a system with a profit factor as low as 1.33 or even lower.
However, the system must be designed for such a profit factor from the very
beginning, constantly taking a similar quantity of both small profits and small
losses. The system above, which goes from a profit factor of 7 to 1.33, has to rely
on one (still) relatively large winner to make up for a large number of losses. This
is a not-so desirable feature in any system.
In fact, given approximately 50 percent profitable trades, to produce an
annual long-term sustainable return of 25 percent, you don’t need a system with a
profit factor higher than 1.5, as the following math will show:
With 50 percent profitable trades, 200 trades, risking $1,000 per trade, a 25
percent return on the risked amount translates into a final profit of $50,000 (0.25
* 200 * 1,000). To make a $50,000 net profit while losing $100,000, the gross
profit needs to be $150,000. A gross profit of $150,000 divided by a gross loss of
$100,000 results in a profit factor of 1.5. With 33 percent profitable trades, 300
trades, risking $1,000 per trade, a 25 percent return on the risked amount translates into a final profit of $75,000 (0.25 * 300 * 1,000). To make a $75,000 net
profit while losing $200,000, the gross profit needs to be $275,000. A gross profit of $275,000 divided by a gross loss of $200,000 results in a profit factor of 1.38.
Granted, such a system isn’t particularly exciting or sexy to trade, but it isn’t
your trading that should be exciting and sexy. It’s the lifestyle you can afford
because of it that should be all that. Note also that the return numbers discussed
so far in this chapter are based on constant-dollar risks and investments. But as we
already know, we should not measure the results in dollars, but in percentages. In
doing so, we start to compound the returns by making use of previous winnings in
trades to come. We will talk more about this in Part 4, where we also will learn
how working with compounded returns helps us tailor the risk–reward relationship
to fit our precise needs and risk tolerances for expected returns.
A SAMPLE STRATEGY ANALYSIS
A very well known trader, system designer, and seminar speaker that I know of
once held a short presentation for a group of traders and analysts, among whom I
was one. Knowing about my work and my book Trading Systems That Work, and
that all the other listeners did as well, she started out the seminar by looking in my
direction while stating smugly, “Percentages, percentages, that is all fine and well,
but the only thing I’m interested in are the dollars. Percentages won’t put bread on
my table; only dollars will.”
She then went on telling the audience that her goal in trading was to make a
net profit of $1,000,000 per year, or a net profit of approximately $4,000 per day.
To achieve that, she started out the trading day by picking out a few stocks that she
52
believed were poised for a four-point move and then bought 1,000 shares of any of
those stocks when the move got started.
When someone asked what she did if she couldn’t find any such stocks, she
answered that she then picked the stocks that were poised for the largest moves and
simply bought more of those stocks, so that the final estimated profit still reached
$4,000. Then someone asked what happened if the stock in question only moved
half the distance. The answer to that was to continue to look for other stocks that
might be poised for a good move and buy enough of those to cover for the amount
remaining, up to the $4,000.
Finally, someone asked what she did when she lost on the first trade, to
which she responded that she now had to find several stocks to trade, or pick one
that was poised for a large enough move to make up for the loss, as well as the
$4,000 still missing in profits. When someone asked where she found these stocks,
she admitted that they where easiest to find among those stocks already priced
above $50. Too-cheap stocks weren’t worth looking at because they never made
moves large enough.
Okay, let’s stop here and ask what’s going on. She’s working with percentages, and she doesn’t even know it! Let’s assume she actually manages to make
$4,000 a day, in which case she’s one hell of a trader. Can you imagine how much
she could be making if she actually knew what she was doing? The sky is the limit.
Her mistake is to only look for moves of a certain point size, instead of
moves of a certain size in relation to the estimated entry price, and then alter the
number of shares bought to reach the estimated profit of $4,000. If she does that,
she will always tie up the same amount of capital in each trade, no matter the price
of the stock.
For example, if stock ABC, which is priced at $80, is poised for a four-point
move, the amount of money she needs to tie up in the trade will be $80,000. If, on
the other hand, stock XYZ, currently priced at $40, is poised for a four-point move,
the amount of money tied up in the trade will only be $40,000. But as we all know
by now, and as the speaker admitted, the lower priced the stock, in general, the
smaller the moves. A $40 stock only needs to move half as much in dollar terms as
an $80 stock, to move the same distance in relation to their respective entry prices.
That is, if you want to give yourself the same chance to make $4,000 out of
a $40 stock as out of a four-point move in an $80 stock, you only have to look for
a two-point move and buy twice as many stocks, so that the amount invested will
be $80,000 for the $40 stock as well. But all this about the price of the stocks and
the number of shares to buy we have talked about already. Given what we have just
learned about the profit and risk factors, let’s instead look to see if this $4,000-aday (or trade) strategy could be something for you.
Let’s assume we have $100,000 to play with. To make $4,000 a day, with 50
percent profitable trades, we need to have a fairly tight stop loss; otherwise, the
winners needed to make up for the losses as well as the desired profits will be
CHAPTER 4
Risk
53
placed too far away from the entry price to be reached within a day. Let’s say we
use a 2 percent stop, also equal to a 2-point move for a stock trading at $100 (1
point for a $50 stock, 1.5 points for a $75 stock, and 0.5 points for a $25 stock,
but because this trader didn’t believe in percentages these numbers don’t apply).
Buying $100,000 worth of a $100 stock means we can buy 1,000 shares.
Therefore, if the trade goes against us, we lose $2,000 every other trade. To make
$4,000 on average over two trades, the winning trade must generate a profit of
$10,000 (4,000 * 2 2,000), or $10 per share, which also equals a 10 percent
move and a 10 percent return on account.
(Note that if the trading ended at that value for the day, the profit would have
been $8,000 for that day. But because both winning days and losing days occur, we
still need to assume that we must make $4,000 on average, per trade. For example,
if the next day were to end in a loss of $2,000, the average profit per day would
now be down to $3,000 [(8,000 2,000) / 2], and we would have to make $6,000
to compensate for that the following day [(8,000 2,000 6,000) / 3]).
First, how often do you see a $100 stock make a 10-point move over a day,
not to mention an even lower priced stock? And how often have you identified it
beforehand, so that you actually had a chance to ride the move? Once or twice
maybe, but not often enough to come even close to make any $4,000 a day. Second,
with the winning trade having to be worth $10,000 to compensate for the $2,000
loss, to make an average profit per trade of $4,000, the profit factor has to be five
(10,000 / 2,000). Third, making $8,000 while risking $4,000 (2 * 2,000), the risk
factor comes out to two, or a 200 percent return on the risked amount. Knowing
what we now know about the profit and risk factors, how likely is it, do you think,
that we will be able to sustain these numbers, day in and day out, over the next several days and months? Not likely at all, I say.
Obviously then, we need to adjust our strategy somehow. Let’s say we adjust
our stop loss to only one point per share, but because of this, the percent of profitable trades decreases to 33 percent, or only every third trade will be a winner.
Now, to make $4,000 on average per trade over three trades, the winner needs to
be $14,000 (4,000 * 3 1,000 * 2). Now the winning trade needs to be even larger, so obviously this is not the way to go, even though we don’t need to find as
many winners as before.
What happens if we go the other way around? Let’s say we set the stop four
points away, so that the percentage of profitable trades increases to 67 percent. In
that case, two winning trades will have to make up for one $4,000 loss, plus an
additional $12,000 profit to make the profit per trade equal to $4,000 (4000 * 3 4000), which means that the profit per trade for the profitable trades needs to be
for $8,000 each. OK, with a total profit of $16,000 and a total loss of $4,000, we’re
down to a profit factor of four and a risk factor of one (12,000 / 12,000).
Obviously, even these numbers are too high to be sustainable, but the only
way to lower them further would be to increase the percentage of profitable trades
54
by placing the stop loss even further away from the entry point. However, no matter how good our system is, it is not likely that we will increase the percentage of
profitable trades that much more. As things are right now, the risk–reward relationship going into the trade is already down to 2:1, the minimum required by most
system builders and traders. So, is there yet another way to make this strategy
more tradable?
Yes, there is, actually: Place both the profit target and the stop loss closer to
the entry price and simply put on larger positions, so that the decreased profit per
share is counteracted by more shares, for a constant average profit per trade of
$4,000. So, what makes sense for a day-trading strategy? Placing the target four
points away from the entry price? Nah, that still feels a little much to be able to
keep up on a long-term sustainable basis. One point? Perhaps a little too tight, considering the stop loss then needs to be only 50 cents away from the entry. Let’s say
that a profit target of two points makes sense. Thus, we’re back where we started,
so to speak, and the stop loss needs to be at one point away from the entry.
To make $8,000 with a two-point target applied on a $100 stock, we therefore need to buy 4,000 shares, for a total of $400,000. Now it all makes sense. We
have counted backwards to come up with the characteristics our strategy needs to
make $4,000 a day and per trade on average, and how much money we need to
tie up in one trade. Now we only need to come up with an actual strategy with a
profit factor of 4, a risk factor of 1, and 67 percent profitable trades. How many
of us have ever come up with such a strategy, which also remained robust when
traded for real on unseen data? Well, I don’t know about you, and I most certainly don’t want to argue against the system designer who apparently has such a
strategy, but I for one have never and will never come up with such a strategy. If
that is the type of strategy you’d like to find in this book, you might just as well
stop reading right now.
Note also that we now need to tie up $400,000 in each trade (not $100,000
as originally stipulated). How many of us have that kind of money to place in one
trade only? And what if we would like to diversify a little? Then we need another
multiple of $400,000 for each stock we’d like to trade. Say you’d like to be in at
least three trades at a time and also have the money available for one additional
trade, just in case. Then you’d need $1,600,000.
What if $100,000 is all we have (which is still a lot of money for many of my
readers), and we would like to be in three to four positions at the same time? Given
that we do have a long-term sustainable strategy with a profit factor of 4, a risk
factor of 1, and 67 percent profitable trades (yeah, right), then how much can we
expect to make per trade and day, on average? The answer is $500 (25,000 / 100 *
2), or approximately $125,000 per year (500 * 250).
The point I’m trying to make with all this is that with only $100,000 at hand,
you need a fantasy system (at least for most of us) to even make what you are making already—especially if you don’t understand how to calculate percentages, the
CHAPTER 4
Risk
55
magic of proper money management (which we address more thoroughly in
Chapter 4), and the power of trading several seemingly less tantalizing systems on
several markets. That is what this book is about.
Before we close this chapter, let me once again draw your attention to Active
Trader magazine, which during the fall of 2001, featured a series of articles by the
renowned systems developer Dennis Meyers, Ph.D. In these articles, Mr. Meyers
showed that the larger the profit factor (above two) during initial testing, the less
likely a system is to hold up in the future, when the system is traded for real or
tested on previously unseen data. In these articles, the system was an intraday
breakout system tested and traded on IBM with five-minute bars.
CHAPTER
5
Drawdown and Losses
The only thing true about trading is that we will all go broke if we just stay at it
long enough. The longer we stay in the game, the closer we get to that one freakish
trading day, week, month, or year when everything goes against us. For some, it
might happen tomorrow; for others, it won’t happen in their lifetime but would have
happened had they been able to trade for another 1,000 years. The trick is to make
this freakish occurrence as freakish as possible. But no matter how freakish we
make it, the chance of it happening at any time (however minuscule) will always be
there, no matter how rigorous we’ve been at putting together our systems.
Most people don’t understand what I mean by this, and meet me with arguments such as, “but I always have my stops in place,” or “I alter my systems with
the market conditions.” But it doesn’t matter what you do: the chance is always
there that at one time everything can and will go against you—whether the situation of bad luck lasts for two seconds or several years doesn’t matter. At some
point, it can and will happen, if you just stay in the game long enough.
One way to look at it is to compare yourself to one of the Highlanders in the
old Highlander movie. These supernatural beings could only die by having their
heads chopped off. Well, there are people getting their heads chopped off all
around the world, all the time, be it by accident or by intent, and if that is the only
way to go for a Highlander, sooner or later it will happen to him as well.
Another way to look at it over a longer period is to compare it to a monkey
in front of a typewriter, typing out Shakespeare’s Hamlet by pure chance. Chances
are slim, but they’re there, and it won’t happen overnight.
By the same token, the old trading adage, “your worst drawdown is still to
come” is equally as true. But it doesn’t have to happen first thing tomorrow, pro57
58
vided you’ve done your homework correctly. Unfortunately, however, very few
systems designers (professionals and amateurs alike) know how to evaluate a system’s drawdown, as the following little story will show you:
As an editor first for Futures magazine and later for Active Trader magazine,
one of my duties was to visit many of the various trading seminars and conferences, held annually around the country. During one of these conferences, I attended a seminar where a very popular and famous system designer talked about
system design and evaluation, and especially about how to limit a system’s maximum drawdown.
One of the most important aspects of system design and evaluation, he
explained, was to keep the drawdown to a minimum. To illustrate his point for the
large and sacredly quiet audience, he first showed a performance summary for a
system with a certain maximum drawdown amount, measured in dollars. Then he
went on explaining how he modified the system to lower this amount, which he
then showcased with yet another performance summary.
Now, this would have been all fine and well had he moved on to talk about
the many aspects of exactly why the second, lower drawdown was better than the
first one. But this never happened. Instead, he went on with example after example for about two hours straight, with most systems altered with a trend filter of
some sort or a fixed dollar–based stop loss. Needless to say, at the end of his seminar, the audience was awestruck by his system-design capabilities and analytical
mind. To me, it was painfully clear that not only the audience didn’t have a clue,
but worse still—neither did the speaker!
DRAWDOWN COMPARED TO EQUITY
To compare two drawdown figures to each other, you simply cannot only look at
these two numbers and say that the lower one is better than the higher one—not
even for two similar systems, traded on the same market, over the same period.
Instead, you must put the numbers in relation to where and when the drawdowns
took place, in regards to both your latest equity peak and the level at which the
market traded.
For example, by altering a system ever so slightly by adding a trend filter, a
drawdown that was caused by a series of long trades when the market was in a
downtrend can be washed away completely. This means that the second, improved
drawdown must have taken place at a completely different time and place, in
regard to both the account equity going into the drawdown and the level at which
the market traded.
Say, for example, that the drawdown for the first, unimproved system was for
$60,000, at the end of a couple of years of good trading that had taken the equity
from an initial $100,000 to $300,000. In that case, the drawdown depleted the trading capital by 20 percent (60,000 / 300,000), leaving you with $240,000. For the
CHAPTER 5
Drawdown and Losses
59
“improved” system, a maximum drawdown of $30,000 might have taken place
right off the bat, depleting the capital by 30 percent (30,000 / 100,000), leaving
you with $70,000.
Now, I don’t know about you, but I would rather have a 20 percent drawdown
leaving me with $240,000, than a 30 percent drawdown leaving me with $70,000.
Hence, everything else aside, the first unimproved system is better than the second improved one, no matter if the end result for the second system was higher
than $240,000. To measure the drawdown in relation to the equity, it might be a
good idea to put together a so-called underwater equity chart like that in Figure
5.1, which shows that the maximum historical drawdown for this particular system
is approximately 5 percent.
DRAWDOWN COMPARED TO THE MARKET
Comparing the drawdown to the equity leading into it only addresses a small part
of the problem. Another important aspect to consider is the level at which the market traded at the time. It should come as no surprise by now that the higher the dollar value of the market, the wider its price swings will be, also measured in dollars.
In that case, a low drawdown, taking place when the market is at a high level,
is preferred over a high drawdown with the market trading at a low level. However,
FIGURE
5.1
Underwater equity chart.
60
provided you go long or short the same number of shares throughout both trading
sequences, a high drawdown still can be better than a low drawdown, if the market also is sufficiently higher in the case of the high drawdown compared to where
it is during the low drawdown.
This is easier to understand if you isolate your drawdown to one single trade.
For example, if a stock is priced at $60, and you buy 1,000 shares and lose $5 per
share, you have lost a total of $5,000 (1,000 * 5), or 8.3 percent (60 * 1,000 /
5,000) of your investment. If, on the other hand, the stock is priced at 30, and you
buy 1,000 shares and lose $3 per share, you have lost a total of $3,000 (1,000 * 3),
or 10 percent (30 * 1,000 / 3,000) of your investment. Thus, even though the higher priced market (and its inherent larger price swings) forced you to invest and lose
more dollars, the fewer dollars lost in the lower-priced market resulted in a relatively larger loss of equity.
Thus, if you apply a trading system that buys or sells a constant amount of
shares on a trending market, the value of the losing (and winning) trades should
be sufficiently lower in a low-priced market, compared to a high-priced market.
That is, the wider the price swings, measured in dollars, the larger the drawdown,
also measured in dollars, should be. If that is not the case, there is something
wrong with the logic behind the system.
One such logical blunder people make all the time is to apply a fixed
dollar–based stop that will have you stopped out after a trade has moved against
you a specified amount. However, the effect of such a stop is that it will have you
stopped out repeatedly on a high-priced market, but hardly ever on a low-priced
market: It will be too tight for the high-priced market, but too wide for the lowpriced market, in relation to the respective markets’ normal price swings.
Furthermore, this system-design blunder can be very hard to detect via the
drawdown because, in the case of the low-priced market, a larger than necessary
drawdown can be a result of a few but larger than necessary losers, while in the
case of the high-priced market, a larger than necessary drawdown can be a result
of a large amount of unnecessarily small losers.
MEAN–MEDIAN COMPARISONS
Another oft-forgotten attribute of the maximum drawdown is how it relates to the
average drawdown. Ask yourself the following questions, “Would I rather experience plenty of tiny drawdowns than a few really large ones?” I think most of us
agree that we prefer even an infinite amount of smaller drawdowns to one large one.
However, when designing and examining a trading system, one large drawdown doesn’t necessarily have to be that bad, as long as you understand what
might have caused it and trust all the other aspects of the system. The trick is to
get a feel for what created this drawdown and how it relates to all the other drawdowns created by the system.
CHAPTER 5
Drawdown and Losses
61
Basically, there are two ways to get a better feel for the maximum drawdown.
One is to calculate the average drawdown and the standard deviations of all drawdowns, and then see where the maximum drawdown fits within this spectrum. The
further away from the average drawdown the standard deviation boundaries are
located, the more dispersed the drawdowns and the less sure you can be about what
to expect in the future. Remember also that all drawdowns will be represented by
either a negative or a positive number (depending on how you measure them), with
zero drawdown being a definitive boundary in either case. Thus, the distribution
of the drawdowns won’t take the familiar bell-shaped curve associated with a normal distribution. (What you really should do in this case is measure the value of
all runs, both positive and negative, from equity lows to equity peaks, and vice
versa.)
Another way to get a feel for the maximum drawdown is to compare it to
both the average value and the median value of all drawdowns. For example, in the
number series 2, 1, 14, 6, 12, the mean is equal to 7 [(2, 1, 14, 6, 12) / 5], whereas the median is represented by the number 6: 2, 1, 14, 6, 12 (sorted: 1, 2, 6, 12,
14). The higher the maximum drawdown is in relation to the median drawdown,
the more of a freak occurrence the maximum drawdown has been, especially if the
average drawdown is closer to the maximum drawdown than to the median drawdown. For the example above, the maximum value being 14, the average value is
much closer to the median value, which indicates that a drawdown of 14 isn’t as
much of a freak occurrence as we would like it to be.
A bad situation occurs when the median drawdown is larger than the average
drawdown. Then the smaller drawdowns are in minority, representing the freak
occurrences, all the more so, the closer the average drawdown is to the smallest
drawdown. To express this mathematically, divide the average drawdown, by the
median drawdown. The higher this value is above one, the more freakish the large
drawdowns behind the large average drawdown. Similarly, dividing the maximum
drawdown by the average drawdown, gives an indication of how large the maximum drawdown is in relation to the average drawdown, with a value of two indicating that the maximum drawdown is twice as large as the average drawdown. An
alternative is to divide half the maximum drawdown by the average drawdown, so
that the 2:1 relationship will be represented by the value one.
Multiplying these formulas with each other gives us a combined value for
how freakish the average drawdown is in relation to the median drawdown, and
how freakish the maximum drawdown is in relation to the average drawdown:
DFI (AD / MeD) * [(MaD / 2) / AD] (MaD / 2) / MeD
Where:
DFI Drawdown freak index
AD Average drawdown
62
MeD Median drawdown
MaD Maximum drawdown
Note, however, that this analysis says nothing about whether any or all of the
different drawdown values fall within tolerable limits in the first place. All this
analysis does is help you decide if the relatively large or relatively small drawdowns are in minority and considered to be the least expected in the future.
Nonetheless, sometimes you could be better off trading a system with a very
large maximum historical drawdown, as compared to a system with a seemingly
more reasonable maximum drawdown, because you know that the very large historical drawdown was due to a freak occurrence that you expect won’t happen again
anytime soon, which is not the case with the seemingly more tolerable drawdown.
As should be clear by now, the largest drawdown, especially if it’s measured in
dollars, says very little about what you can expect from your system in the future. In
fact, because the drawdown is a function of other system characteristics, rather than
a core characteristic in itself, the best way to come to grips with it is to analyze and
modify these characteristics, instead of trying to modify the drawdown directly.
More specifically, the drawdown is a function of the mathematical expectancy (i.e., the average profit per trade) and the percentage of profitable trades. Table
5.1 shows how it all ties together.
Using the information from Table 5.1 and the DFI, you can analyze the maximum drawdown for a system in relation to the core system characteristics before
you set out to trade your way into any unpleasant surprises, or perhaps even start
to trade a system that you otherwise would have discarded because of the high historical drawdown.
For example, if the system characteristics indicate that the system you’re
examining (whether the results are for real or back tested) has a high average prof-
TAB LE
5.1
Mathematical Expectancy and Percent Profitable Trades
Percent profitable trades
Low
Low
High
Average profit per trade
High
Many and steep made up of
many trades
Many and shallow made up of many
trades
Can take time to get out of
Usually needs only one or a few trades
to get out of
Few but explosive and deep
Few and shallow, with few trades
Can take time to get out of
Easy to get out of with one or a few
trades
CHAPTER 5
Drawdown and Losses
63
it per trade and a high number of profitable trades, but also a very high DFI, you
can conclude that the maximum drawdown most likely was a freak occurrence that
will not repeat itself in the near future. On the other hand, if both the average profit per trade and the number of profitable trades are low, and are also combined with
a low DFI, you can conclude that no matter the actual size of the drawdowns experienced so far, you’re lucky to still be in the game and should not trade this system
for another day. Note also, that in the first example I use the words “most likely.”
This is because, no matter how rigorous your testing has been, there are no guarantees. As already stated, every drawdown will be surpassed at one time or another. All we can do is to make the likelihood of that happening tomorrow as small as
possible.
TYPES OF DRAWDOWN
The drawdown should by no means be neglected completely, but in researching,
you need to know what it is you are doing and what it is you are investigating. For
one thing, the estimated largest drawdown holds valuable information about how
large your account size must be and can give you an indication of whether you
have the psychologic profile to trade the system in question. The several different types of drawdowns all need to be dealt with in a different manner. I have discussed these in detail in Trading Systems That Work, so I will only touch on this
subject briefly here.
Aside from not putting the drawdown in relation to the market situation at the
time, another major error most system designers make when they are building and
evaluating systems is to look only at the overall total equity drawdown (TED),
which is calculated using both the open trade profits and losses, and the already
closed out equity on your account. However, to fully investigate the drawdown, we
also need to divide the TED into several subcategories, namely the start trade
drawdown (STD), the end trade drawdown (ETD), and the closed trade drawdown
(CTD). To understand why, look at Figure 5.2 and follow along in the following
example:
Let’s say that you currently don’t have any positions on and that your last
trade was a $3,000 winner that also took your account to a new total equity high
of $10,000. But before you managed to exit the position, it gave back $1,000 of its
open equity, so that your equity currently stands at $9,000 (day 0 in Figure 5.2).
According to most analysis packages, this means that, even though you managed
to add $3,000 to your closed-out equity, you now are $1,000 in the hole when
compared to your latest total equity high. Furthermore, if your next trade turns out
to be a loser, that immediately stopped out with a $4,500 loss, your closed-out
equity now is $4,500, and your drawdown is $5,500 (day 1). If you then have a
$5,000 winner which, before it took off started out going the wrong way with an
additional $1,000 loss (day 2)—at which point you would have been $6,500 in the
64
FIGURE
5.2
Total equity drawdown (TED) and subcategories.
hole—and then gave back $1,500 of the open profit, your total equity drawdown
would now be $1,500 (day 4).
If you look closely at these numbers, they consist of three different types of
drawdowns. At day 0, we are dealing with the ETD, that tells us how much of the
open profit we had to give back before we were allowed to exit a specific trade. At
day 1, we are looking at the CTD that measures the distance between the entry and
exit points without taking into consideration what is going on within the trade. At
day 2, we are dealing with the STD, that measures how much the trade went
against us after the entry and before it started to go our way. And at day 4, we again
have the ETD.
Of course, we would like to keep all these drawdown numbers as small as
possible, but when only examining the overall drawdown number (the TED) and
blindly trying to do something about it, there is no way of knowing what it is we’re
really doing and what is actually changing within the system when we’re making
any changes to the input parameters.
To be sure, in recent years a few system developers and market analysts have
addressed this issue in various ways, but as far as I know, nobody has really nailed
CHAPTER 5
Drawdown and Losses
65
it down when it comes to how one must go about examining the markets and the
systems in an appropriate and scientific fashion. One of these analysts is John
Sweeney, who, in his two books Campaign Trading (Wiley Finance Editions,
1996) and Maximum Adverse Excursion (Wiley Trader’s Advantage Series, 1997)
came up with the concepts of maximum adverse excursion (MAE) and maximum
favorable excursion (MFE). More recently, RINA systems has taken this further
and developed a method to calculate the efficiency of a trade. I, too, have written
several articles on closely related topics for both Futures magazine and Active
Trader magazine.
Depending on what type of entry technique you use, many of your trades will
experience an STD before they start going your way. This is especially true for
short-term top and bottom picking systems, where you enter with a limit order. In
this case, the only way to avoid an STD is to enter at the absolute low or absolute
high—and how often will that happen?
Longer-term breakout systems also many times experience both an STD and
an ETD when they enter and exit with a stop order on the highest high or lowest
low over the lookback period. Usually, the entry level coincides with a pivotal
resistance or support level in the market. After this level has been tested and
you’ve entered the trade, the market usually makes yet another correction before
the final penetration, and follow-through takes us away in a major trending move.
At the exit, most long-term systems give back a substantial part of the open profit before the exit is triggered by a breakout in the opposite direction.
(To learn more about the different types of drawdowns and the maximum
excursion analysis for stop placements, see Trading Systems That Work. We will
talk more about stops and exits in Part 3 of this book, but will focus on techniques
and analysis methods different from those in Trading Systems That Work.)
CHAPTER
6
Quality Data
A
ll that we have talked about so far matters very little, however, if we don’t have
the right and appropriate data to work with. The truth of the matter is that several
of the largest data suppliers have it all wrong. Look at Figure 6.1, which shows the
closing price of Microsoft as it actually was reported back in 1986, Microsoft’s
first year as a listed company. Note how it wiggles and squiggles, with hardly any
two adjacent closing prices being the same. (I downloaded this data myself from
Microsoft’s Web site.)
Now, look at Figures 6.2 and 6.3, which are taken from two different and
very popular data providers. These charts show their respective versions of how
the Microsoft stock moved during its first year traded. The charts differ from the
one in Figure 6.1 because of the added high and low prices, but two important
things must be noted here: First, because the Microsoft stock has been split several times, the price of the stock in these charts is much lower. This is all fine and
well and can be dealt with, using proper system testing and design.
More alarming, however, is the fact that most of the wiggles and squiggles
are gone: Instead, the closing price seems to jump between a few very distinct
price levels. For each split, these data vendors also adjusted the new and lower
split-adjusted price to match the nearest tradable fraction. For example, if the historical stock price came out to $4.76, it was adjusted down to $4.75, because
$4.76 was not a tradable price. Over time and many stock splits, this smoothed
out the data. Note also that even these charts differ—one of the data providers
hasn’t even done the smoothing correctly. Figure 6.4 shows the data from yet
another data provider. Although this is not as bad as the other two, it still doesn’t
look perfect.
67
FIGURE
6.1
Microsoft trading data—1986. Actual performance.
FIGURE
6.2
Microsoft trading data—1986. Version 1.
68
FIGURE
6.3
FIGURE
6.4
69
70
Obviously, the data providers behind the data in Figures 6.2 and 6.3 thought
that they were doing me a favor by not letting me believe that Microsoft traded at
the impossible price of $4.76, so that I wouldn’t go and build myself a strategy that
tried to trade Microsoft at that price. Therefore, in an effort to make things as realistic as possible, they adjusted the price to the closest tradable fraction. But this is
all wrong and backwards thinking. Because no matter at what level Microsoft
actually traded several years back, or no matter what the true split-adjusted price
is (or the split-adjusted price that these data providers provide me with), I can’t
turn back time and go trade Microsoft at any of these prices anyway. What interests me is to see if I can come up with a way to catch the wiggles that the Microsoft
stock created at that time and that it continues to produce today.
All I am interested in, as an analyst, is examining if my system in fact manages to catch the wiggles and squiggles as they actually took place. For this, it
doesn’t matter what the actual price of the stock is pre- and post-splits. What is
important is that the relationship between price points stays the same. Clearly,
they do not in Figures 6.2 and 6.3. Therefore, these data are useless for historical
testing.
We are not interested in “realistic” back testing in dollar terms, because we
can’t trade at those dollar values anyway, no matter how much we want to, because
they represent foregone opportunities. The best we can do is use data in such a way
so that we make our back-tested results as robust and forward-looking as possible.
And the way to do that, as we already know, is to work with percentage moves and
normalized results.
With percentage moves, the distance between point A and point B relates to
point A exactly the same, no matter the price of point A. Look at the two charts of
Microsoft, by Microsoft (Figures 6.1 and 6.5). They are identical, except for the
difference in price. The price differences are because of stock splits, but no matter
the price before and after the split, each price level relates to all the other levels
the same way in both charts. Thus, in the split-adjusted chart, the price might seem
to have been low, but it behaves as it did when it was higher.
That last sentence is very important to understand completely and fully,
because in Part 3, we talk about the various methods for placing stops and exits.
For now, let’s just mention briefly that many system builders think that the lowerpriced the stock, one should work with wider stops, relative to the entry price.
They believe that lower-priced stocks are more volatile than higher-priced stocks,
and therefore they need a little extra leeway. There might be something to that reasoning, but for system testing purposes, it is no good, because, as we have just discovered, even though a stock seems to be priced as low as 20 cents, it still can act
as if it were trading at $80, because this was the actual level at which the trading
took place in the first place, with the 20-cent level implemented long after the fact.
Therefore, no matter the price of the market, each stop must relate to its entry
price exactly the same way as all the other stops, no matter which entry price each
CHAPTER 6 Quality Data
FIGURE
71
6.5
Microsoft trading data—1986. Microsoft’s performance data.
stop relates to. And the only way to achieve that is to work with percentage-based
(normalized) calculations.
A SCARY FUTURES-MARKET EXAMPLE
If you are a commodity futures trader, one of the main obstacles when testing trading strategies on historical data is the limited life span of a futures contract. To
overcome this, various methods on how to splice several contracts together to form
a longer time series have been invented. This is especially important when it comes
to making your system reports as forward-looking as possible, and if you would
like to use the percentage-based calculations described earlier.
Basically, three different methods can be used to splice contracts together:
the nonadjustment method, the back-adjustment method, and the perpetual adjustment method. The back-adjustment method can further be subdivided into pointbased adjusted and ratio adjusted. (All these methods are described in greater
detail in Trading Systems That Work.)
72
Using the nonadjustment method, you simply stop charting one contract
when it expires, or when you otherwise deem it justifiable to do so, and continue
to chart the next contract in line. This contract is the new front contract. Usually,
this coincides with when the market as a whole moves from one contract to the
next, resulting in an increase in the open interest for the new front contract surpassing the open interest for the old contract.
The main advantage with the nonadjusted time series is that it shows you exactly how the front contract was traded at that particular time, with all trading levels and
price relationships intact and exactly as they once appeared in real life. Figure 6.6
illustrates what this looked like for the December contract on the S&P 500 index
during the crash of 1987. From a high of 333 on October 2, the market fell a total of
152 points, or $38,000 (152 * 250), to a low of 181 on October 20. In percentage
terms, this equals a drop of 45.6 percent (152 / 333) of the total market value.
The main disadvantage of the nonadjustment method is the differences in
price that frequently appear on the day for the roll; these distort your back-testing
FIGURE
6.6
S&P 500 December contracts—crash of 1987.
73
results. Therefore, nonadjusted data are best for day traders with very short trading
horizons, who more often than not close out all their trades at the end of the day. To
overcome the distortions on the historical system’s testing results induced by the
nonadjustment method, the point-based back-adjusted contract was invented.
If the new front contract is trading at a premium compared to the old contract, the entire historical time series leading up to the roll will be adjusted upward
with that distance. A similar but opposite adjustment takes place each time the new
contract is trading at a discount. Figure 6.7 shows what the October 1987 market
action looks like using a point-based back-adjusted contract, with the latest roll
made in September 1999. In this chart, the high on October 2 is at 567.35, and the
low on October 20 is at 415.35, for a total difference of 152 points. However,
because of the transition upward, the original percentage difference of 45.6 percent now has decreased to 26.8 percent (152 / 567.35). For each roll, all these values continue to change slightly, presumably upward, resulting in an
ever-decreasing percentage difference.
FIGURE
6.7
October 1987 using point-based back-adjusted contracts.
74
This continuing decrease (increase) of the relative importance of historical
moves in an up trend (down trend) and markets that are traded at a premium (discount) is the main disadvantage of the point-based back-adjusted contract. For
instance, if the 26.8 percent drop—as implied by the back-adjusted contract—
were to be used to calculate the dollar value of the drop from the actual top of 333,
we would come up with $22,311 (0.268 * 333 * 250) instead of $38,000 (0.456 *
333 * 250). Therefore, to keep the relative importance of all historical moves constant, these moves must be viewed in percentage terms.
In an article for Futures magazine (“Data pros and cons,” Futures, June
1998) and later in a second article (“Truth be told,” Futures, January 1999), I suggested that a better way to adjust a spliced-together time series would be to use
ratio adjustments rather than points or dollars. In doing so, this new time series
will also vary in levels when compared to where the true contract was traded, but
instead of keeping the point- or dollar-based relationship between two points in
time intact, the percentage relationship will stay the same.
FIGURE
6.8
October 1987 using ratio adjusted data (RAD).
75
Figure 6.8 shows what the October 1987 crash looks like through the perspective of the ratio adjusted data (RAD) contract, with the latest roll made in
September 1999. This time, the high of October 2 is at 486, and the low of October
20 is at 264.15, for a point difference of 221.85 points, but with a percentage difference once again equal to 45.6 percent [(486 264.15) * 100 / 486]. This
increase in magnitude measured in points is due to the upward transition because
of the many rolls. The important thing is, however, that the percentage-based move
stays intact at 45.6 percent.
To get a better feel for the benefits of the RAD contract, let’s compare it to
the drop during the fall of 1998, which became the new dollar-based record drop.
During October 1987, the market fell 152 points, or $38,000, or 45.6 percent—
this we know. During the fall of 1998, the market fell from a July high of 1199.4
to an October low of 929, for a total drop of 270.4 points (as measured on the
nonadjusted contract). In dollar terms, this equaled a drop of $67,600 (270.4 *
250). That is, almost twice as much as the October 1987 drop. In percentage
terms, however, the drop of 98 only equaled 22.5 percent of total market value.
That is, the drop in 1998 was not even half as bad as the crash of 1987. In fact,
to equal the crash of 1987 in relative terms, the 1998 drop would have had to continue all the way down to the 652.5 level, for a total drop of 546.9 points, or
$136,725.
Thus, the crash of 1987 is still the largest relative drop in equity in modern
times (aside from the latest bear market in NASDAQ). And, if you, in your system
building and analysis work, would like to treat it as such to make your systems
more robust and give them a better chance to hold up in the future, the only way
to do that is to use the RAD contract in combination with the percentage-based
performance measurements described earlier.
Another major advantage of the RAD contract is that it can never go negative, which can happen with the point-based contract. The major disadvantage of
the RAD contract is that it’s not supported by any major analysis software packages, although it is supported by a couple of data providers, such as CSI data
(www.csidata.com) and Genesis data (www.gfds.com). To calculate the values for
the RAD contract yourself, using the nonadjusted contracts as a base, you can use
the following formula:
NPOC OPOC * [(PNC OPOC) / PNC 1]
Where:
NPOC = New price of old contract
OPOC = Old price of old contract
PNC = Price of new contract
76
UNDERSTANDING PROFITABILITY
In this first part of the book, we have learned that, to build good and profitable
trading systems, there are a lot of things to think about. One thing we need to
understand is the huge difference between a good trading system and a profitable
one. Any good trading system can be made into a profitable trading system when
traded on the right market or portfolio of markets, or together with other good
trading systems. The paradox is, however, that not all profitable trading systems
have to be good systems. Most systems will and can be profitable at one time or
another and just because a system is profitable here and now doesn’t mean that it
is a good system.
To understand this, we must understand the difference between the terms
“good” and “profitable” when it comes to system testing and design. A good system is a system that works, on average, equally as well on several different markets. It isn’t always profitable on all of them, but being so on average over time
ensures it is robust and will generate a steady profit over time, when applied to the
right markets. Some markets should not be traded with certain types of systems:
The moves the system aims to catch aren’t profitable enough to make trading
worthwhile on that particular market. A good system that is worthwhile trading on
a market to generate a profit from that market also is a profitable system on that
very market.
To build a good system, we must make sure that the system catches the types
of moves it is intended to catch, no matter where and when those moves took
place, in relation both to time and the current price of the market. To do that, we
must normalize the system’s results in such a way that all back-tested trades get an
equal weighting. This can either be done by always trading one contract only and
measuring the results in percentage terms, or by always trading a fixed dollar
amount so that the number of shares will vary with the market price (higher price,
fewer shares, and vice versa). Only by doing this will a profitable trade in a lowpriced market influence the final parameter setting to the same degree as a profitable trade in a high-priced market.
Also, during this initial research, we should not consider the cost of trading,
such as slippage and commissions. We’re only interested in finding out if the system is efficient enough to catch the types of moves on the chart that we want it to
catch. The efficiency is measured in the average profit per trade, which should be
high enough to warrant trading with the costs of trading taken into account. Taking
the costs of trading into account at this initial stage of the testing procedure will
only favor more long-term systems, using few trades that seem to be particularly
profitable on high-priced markets.
However, to do our research correctly, we also must be careful about the data
we use. Many data providers have rounded the data to the nearest tradable fraction
of price after a stock has made a split. After several splits, this error compounds
77
over time, resulting in a data series that is far from being representative of the way
the stock actually traded at the time, before the splits took place.
The efficiency of a system is mainly measured via the average profit per trade
in normalized terms. It is better to look at the average profit per trade, rather than
the final net profit, because it is the final net profit that is a function of the outcomes of the many trades, instead of the other way around. The average profit per
trade is also called the mathematical expectancy of the system. From this, it follows
that for a system to be profitable, the mathematical expectancy must be positive.
However, because the outcome of any individual trade most likely will not
be the same as for the average trade, it also is important to know how much all
trades are likely to deviate from the average trade. This measure is called the standard deviation and is a measure of the risk involved in trading the system. The
higher the standard deviation, the less sure we can be of the outcome of any individual trade, and the riskier the system. Dividing the average profit per trade by
the standard deviation of all trades gives us the risk-adjusted return. The higher
the risk-adjusted return, the higher the average profit in relation to the risk of
trading the system.
It also is good to know the normalized values of a system’s average winner
and loser. In the best of worlds, the losers only have one size—that of the stop
loss—which makes the average loser equal to the largest loser. Knowing this, we
can calculate a system’s true risk–reward relationship and experiment with different types of profit-taking techniques, such as profit targets and trailing stops, to
create a trade profile that suits our needs.
Managing your trades this way also means that most trades should fall within a few very distinct categories, the two most obvious being the maximum winner
and the maximum loser. The distribution of your trades should not follow the regular normal distribution, which implies that the outcomes are random. The monthly results, however, could follow a normal distribution around a positive mean.
Knowing the size of the average winners and losers also makes it possible to
calculate a realistic number of trades to get out of a drawdown. Adding the average time spent in a trade to this equation also makes it possible to calculate a realistic time horizon for the same dilemma.
Talking about drawdown, it is a sad but true fact that your worst drawdown
is always still to come. No matter how severe your worst historical drawdown is
today, if you only stay in the game long enough, another drawdown will occur that
will surpass it, both in time and in magnitude. From this, it also follows that if you
only stay in the game long enough, you will encounter a drawdown that will be
deep or long enough to take you out of the game completely.
The only thing we can do about this is to make the likelihood for these drawdowns as small as possible, so that, statistically speaking, it shouldn’t happen anytime within, say, the next 1,000 years or so. But even so, and no matter the
precautions, for some it can and will happen tomorrow, simply because of bad luck.
78
To come to grips with drawdowns, we need to put them in relation to both the equity peaks preceding them and the value of the market at the approximate time of the
drawdown.
But even more important, we need to understand that the drawdown is not a
main system characteristic, but rather a function of the average profit per trade and
the percentage of profitable trades. By focusing on these numbers and making
them as high and as robust as possible, we’re also minimizing the risk for any devastating drawdowns. It is, therefore, important to get a feel for the number of winning and losing trades in a row that a system is likely to encounter and how likely
it is for a similar sequence of trades to happen again.
However, boosting these and other performance measures to sky-high levels
isn’t necessarily a good thing either. Instead, we need to work with numbers that
are reasonable, when compared to other investment or trading opportunities and
the way the market actually behaves. For example, a system with a profit factor of
two and 50 percent profitable trades also has a return of 50 percent on the total
capital risked, whereas a system with a profit factor of 1.5 and 33 percent profitable trades has a return of 33 percent on the total capital risked. For two systems
to produce results like this, they need to have initial risk–reward relationships,
going into their trades, of 2:1 and 3.5:1, respectively.
If we compare these return numbers with other investment opportunities and
the way the market behaves, we realize that this is as good as it will get, and that
looking for systems with higher profit factors results in impossible initial
risk–reward relationships. If the initial risk–reward relationships aren’t sustainable
in the long run, the future performance of the system will plummet. This might
result in a system that still produces a decent profit factor, but has other system
characteristics making it untradable, such as an unreasonably high percentage of
losers and a high standard deviation to the outcome of the trades.
Tying all the above together and making an analogy with the animal kingdom, it probably is fair to say that most of us would like to trade a system behaving like a cheetah—a mean, lean, killing machine. However, because the cheetah
is too dependent on its environment for its survival, trading a system that behaves
like a cheetah is not a good idea, because even small changes in its environment
will lead to its extinction. Instead, a trading system should behave like a cockroach
that can live and eat almost without concern for the rest of the world.
In trading system terms, the system should function equally as well on average over as many markets as possible, grinding out small profits wherever possible and staying afloat during tougher times. Granted, there is little sex appeal to
such a system. But it isn’t your trading that should be sexy, but rather the lifestyle
you can afford because of it.
PART
TWO
Trading System Development
I
n my opinion, coming up with a smart system idea to trade the markets is a little
like composing a new piece of music. To the untrained ear, it seems as if there are
only so many notes, tones, and octaves to go around, so that all their possible combinations should be exhausted by now. Similarly, to the untrained eye, there seem
only so many different short-term bar combinations on a chart and indicators to
combine them with. But even so, a lot of people are coming up with new music all
the time, just as a few market technicians have the ability to come up with new
short-term trading patterns.
Although most of the patterns and systems in this part are of my own creation,
the ideas behind them are not. In my former positions as a writer for Active Trader
magazine, and before that Futures magazine, I often found myself in a situation
where I had tons of good ideas presented to me, ready to run, with very little or no
additional effort on my part. Many of the systems here are the fruits of such ideas.
One of those who seems to come up with one great idea after another is
Michael Harris, who, in a couple of articles for Active Trader magazine, presented the Harris 3L-R pattern variation, featured in Chapter 14. Another never-ending source for inspiration is Tom DeMark, who gave me the idea for the expert exit
system, featured in Chapter 15. The system presented there isn’t Tom’s, but the
idea for it came to me after having read his material and discussed a few concepts
with him.
Yet another great source for inspiration is my friend Mark Etzkorn, the editor-in-chief of Active Trader magazine. Mark is a swing-trading guy who came up
with the concepts and ideas behind the hybrid system in Chapter 8. And behind
Mark lurks Linda Bradford-Raschke, who most certainly has proved herself, both
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PART 2
as a great developer of swing-trading strategies and good friend and inspirational
source for both of us.
For the relative-strength type systems, no inspirational source is greater than
Nelson Freeburg. Nelson’s systems usually follow a more long-term investor-like
philosophy, which makes it more natural for him to think in terms of the rotation
of assets based on relative strength and momentum.
Finally, no cooler trader exists than Dan Gramza. Without my discussions
with Dan, I would not have been able to develop my own philosophies surrounding where, how, and when to look for an exit, no matter which system I’m working on. This is especially true when it comes to the time-based stops for trades that
go nowhere. Dan knows how to not get married to his trades.
All systems presented in this book can be divided into four different system
categories, with a few of the systems belonging to several of these categories. In
the retracement and swing trading category, I count hybrid system No. 1, meander
system V. 1.0, the volume-weighted average system, the expert exits system, and
the Harris 3L-R pattern variation system.
Of these systems, the meander system is the only one using limit orders for
the entry. In fact, it’s one of the few systems I have ever seen that produces consistent results using limit orders. This system is based on my favorite indicator,
which I developed during my time with Futures magazine and while writing my
first book, Trading Systems That Work. I like that meander is both scientifically
correct and at the same time well suited for short-term trading. The logic and reasoning behind meander is not based on any homemade technical analysis mumbo
jumbo. Because I like this indicator so much, I also have tinkered around with it
quite a bit. Therefore, the code presented here is not the code presented with the
system in Active Trader magazine. The function and the logic are the very same,
but this version runs much smoother and faster, and also holds the possibility for
altering the lookback period for the calculations, which the first version did not.
This is one of the best limit-order systems I’ve ever seen.
Another system that had a very scientific approach to its development is the
expert exits system. This system is interesting because I developed the exit rules
using the same type of surface charts I discuss in greater detail in Part 3. Using
this technique, there is no way you can optimize the system to any specific market, type of market, or market condition. Instead, you’re bound to end up with a
system that will work, on average, equally as well over all types of markets and
market conditions. Whether it is profitable enough for you to trade is a different
story, but no other system will beat a system developed in this way when it comes
to robustness and stability.
Another cool concept among these systems is the volume-weighted average
system, which basically first calculates a stochastic indicator for the volume, multiplies that stochastic value by today’s price, and adds it to a running total, very
much in the same way as a regular exponential moving average is constructed.
PART 2 Trading System Development
81
The volume-weighted average system also belongs to the volume-related
systems, together with RS system No. 1, which really doesn’t care that much about
the price of the market that is about to get traded, other than how the momentum
of the price compares to a comparable index. This system also is a so-called
relative-strength system and also belongs to that group of systems, together with
the relative-strength bands system and the rotation system; as such, it stands out
among these three systems as the only one where the market to be traded is compared to an index (which otherwise is the most common way to do it) instead of a
group of other markets, as the other two systems do.
The relative-strength bands and rotation systems are a little different from
most relative-strength systems in that they compare the stock in question with several other stocks, rather than a comparable index. For this book, I picked all stocks
completely at random, but for your own research, I suggest you group them
according to sectors and industry groups. It also is possible to trade various indexes against each other and thereby set up market-neutral positions, or positions that
are more or less biased according to your current beliefs about the market. In this
part of the book, I look at all the relative-strength systems individually, but in Parts
3 and 4 we primarily use them as filters together with the other systems.
For the relative-strength bands system, an error appeared in the original text
in Active Trader magazine. Instead of computing the Bollinger bands for the RSL
lines, as originally stated, the bands should be computed on the product of all RSV
lines (PRSV). The original code did it correctly, but the original system logic
explained it incorrectly.
Among the breakout systems, the hybrid system No. 1 seems to have withstood the test of time very well. This was one of the first systems featured in Active
Trader magazine. When I put it together, no one knew how severe the subsequent
bear market would be and, being busy with other things, I did not look at it again
until it was time to write this book.
By the way, none of these systems is picked because of their extraordinary
profits or anything like that, but rather only because they represent different concepts and learning experiences. As a matter of fact, as I re-do the research, it’s
apparent that most of them have not coped all that well with the most recent bear
market. As such, they also represent additional challenges for getting back in
shape (more about this in a little while).
One of the systems that I had to tweak most was the Harris 3L-R pattern
variation; although not because it hadn’t held up over time. Rather, the original
logic for the system called for a profit target too far away from the entry price,
which made it too long-term in nature. This, however, had nothing to do with the
original and clever entry idea by Michael Harris.
Over the next several pages, I indulge in a lot of tweaking and modifications
to the original systems, which some of you might call curve fitting after the fact.
I do not call it that, however, and my arguments for that are several. First, I am not
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PART 2
optimizing the systems, but rather trying to find the most robust solution that
should work on average equally as well on as many markets as possible, without
really taking the actual profitability into question until the very last moment.
Second, the little “optimizing” I do (if you still call it that), is very coarse and
based more on my own reasoning and understanding of the systems’ underlying
logic than on actually stepping through each and every input combination. Finally,
the systems are tested on as many as 65 different markets, and I don’t care which
markets the systems are profitable on or not, or on which markets the systems will
be traded in the future.
There are ways to decide that as well, among which one major way is to study
the correlation between all systems and markets and the portfolio as a whole. We
will talk more about this in Part 4, so for now I will only say that sometimes it is
a good thing to trade a losing market. More specifically, when the losing market
still behaves in a way that it performs well when the portfolio as a whole performs
badly, it will decrease the risk for the overall portfolio and sometimes even add
positively to the bottom line. In this case, the risk is measured in standard deviations away from the average equity growth, both for the portfolio as a whole and
for the individual market.
In all the research done in this part of the book, I have not deducted any
money for commissions. As already discussed in Part 1, the most important thing
for now is to see how well the improved or altered systems capture the moves they
are intended to catch, no matter the values of the moves in dollars. Our focus is to
make sure that the average profit per trade is large enough to make trading worthwhile, knowing that the commissions need to be considered at a later stage. We
will, however, deal with this in more detail in Part 4, so in the end, all results will
be burdened with the cost of trading.
Another parameter that will be of importance during this stage of the testing
is the time spent in the market. The more time each individual stock spends in a
trade, either the fewer stocks we can be in simultaneously or the smaller each position has to be. But the fewer the shares in each position, the greater the risk per
share must be for the entire position to reach the desired risk level as a specified
percentage of the overall equity. Consequently, if the risk per share is too large, it
won’t make sense for a short-term trading strategy. Therefore, the trade length and
the amount of time spent in a trade need to be in proportion to the amount risked
per share. We have already touched on this subject in Chapter 1 and will work with
it extensively again throughout Parts 3 and 4.
Before we move on, I would like to point out that the TradeStation code following each system modification is the code for the modified version of the system that I decided to take with me to Parts 3 and 4.
CHAPTER
7
TradeStation Coding
A
s most of you who have followed my work over the years know, I prefer to work
with TradeStation. Currently, I use the 2000i version, which is the second to last
version of the program. I prefer TradeStation because, although the program certainly has its fair share of idiosyncrasies and annoying “features,” it is the only offthe-shelf analysis platform I know of that allows you to, at least partially, work
around these shortcomings by adding your own code.
For example, no program allows me to do the type of portfolio-based money
management I would like to do. Therefore, I need to do all my portfolio management and analysis in Excel or with the help of Visual Basic, and TradeStation is
the only program I know of that allows me to export the data I need into a text file
for further analysis the way I like to do it.
I know of a few new programs out there that have started to allow portfolio
testing and analysis, but so far, I haven’t found one that completely satisfies my
needs or allows me to develop my techniques further. There might be such a program available, but I only have 24 hours to spend per day, and I simply haven’t had
the time to shop around, much less figure out how it works. Therefore, we’re stuck
with TradeStation this time around as well.
I almost feel the need to apologize for that, but on the other hand,
TradeStation’s EasyLanguage code isn’t all that hard to understand if you give it a
serious effort. More often than not the code is in plain English, with the addition
of a set of regular mathematical expressions and signs. I truly believe you’re doing
yourself a great favor if you try to decipher the code, whether you’re a
TradeStation user or not. Once you get used to it (which shouldn’t take long), I’m
sure you will find that many times it’s even easier to understand how a system
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PART 2
works by looking through the code instead of reading through the spelled-out logic
and rules.
To assure robustness and reliable results, with only a couple of exceptions, I
did all the research on 63 different markets. The entire testing portfolio consists of
the 30 stocks making up the Dow Jones Industrial Average, the 30 highest capitalized stocks on the NASDAQ 100 index, and five major market indexes. Because
Intel and Microsoft belong to both the Dow and the NASDAQ groups, they have
been used twice, for a total of 65 test runs per system (see below).
Because of the latest bear market, many of the NASDAQ stocks might no
longer belong to the group of the highest capitalized stocks. But this was the group
I started out with, this is the group I will continue to use. The two systems that
haven’t been tested on the complete portfolio are the relative-strength bands and
rotation systems, which have been tested on 25 markets each.
The 30 Dow stocks are: Alcoa (AA), American Express (AXP), Boeing
(BA), Citigroup (C), Caterpillar (CAT), Dupont (DD), Disney (DIS), Eastman
Kodak (EK), General Electric (GE), General Motors (GM), Home Depot (HD),
Honeywell (HON), Hewlett-Packard (HWP), IBM (IBM), Intel (INTC),
International Paper (IP), Johnson & Johnson (JNJ), JP Morgan (JP), Coca-Cola
(KO), McDonalds (MCD), 3M (MMM), Philip Morris (MO), Merck (MRK),
Microsoft (MSFT), Procter & Gamble (PG), SBC Communications (SBC), AT&T
(T), United Technologies (UTX), Wal-Mart Stores (WMT), and Exxon Mobil
(XOM).
The 30 NASDAQ stocks are: Altera (ALTR), Applied Material (AMAT),
Amgen (AMGN), Bed, Bath & Beyond (BBBY), Concord Computing (CEFT),
Chiron (CHIR), Comcast (CMCSK), Cisco Systems (CSCO), Dell (DELL), eBay
(EBAY), Flextronics (FLEX), Genzyme (GENZ), Gemstar (GMST), Immunex
(IMNX), Intel (INTC), JDS Uniphase (JDSU), K L A Tencor (KLAC), Linear
Technologies (LLTC), Microsoft (MSFT), Maxim Integrated (MXIM), Nextel
Communications (NXTL), Oracle Systems (ORCL), Paychex (PAYX), People
Soft (PSFT), Qualcomm (QCOM), Siebel Systems (SEBL), Sun Microsystems
(SUNW), Veritas Software (VRTS), WorldCom (WCOM), and Xilinx (XLNX).
The five stock indexes are the S&P 500, S&P 400 Midcap, NASDAQ 100,
Dow Jones Industrial Average, and Russell 2000.
I used no futures markets for this research, for two reasons. First, up to this
point I have only worked with stocks when building the systems for Active Trader
magazine. Second, when I wrote Trading Systems That Work, I worked exclusively with futures contracts, which made the book a little hard to grasp at times for
those who only trade stocks. However, most, if not all, of these ideas should be
applicable on all types of markets, so if you’re a futures trader, you should have
little problem transferring these ideas to the futures markets of your interest.
Whether the system will be profitable on any particular market is, however, a completely different story. As already mentioned, I don’t care so much if the system is
CHAPTER 7 TradeStation Coding
85
profitable on all markets tested as long as it works, on average, well on a majority of them.
Note that because Intel and Microsoft belong to both the NASDAQ and Dow
groups they have been used twice throughout the research, which means that the
results from these markets carry twice the weight compared to all other markets
when it comes to the final influence of the system variables. Of course, it would
have been a little better had I substituted for both these stocks other stocks in the
NASDAQ group, but because I am using so many stocks and indexes in the first
place, it doesn’t matter that much.
For example, with 65 markets, each market influences the end result by 1.54
percent (100 / 65), which means that Intel and Microsoft influence the end result
by 3.08 percent each, or 6.16 percent in total. In turn, this is only onesixteenth of the total weight. It turned out this way simply because this was the
way my workgroups were set up for testing my systems in Active Trader magazine,
where I only test one group at a time.
It doesn’t take a rocket scientist to recognize that there are significant differences in the characteristics for the stocks of the Dow Jones Industrial Average
compared to the stocks of the NASDAQ 100 index. For one thing, for each system
lab, I also show the latest development for the major market indexes as a comparison to the system’s results. For one of the latest systems I did (September 2002
issue, using data through April 2002), the Dow had increased by 206 percent since
September 1992, but was currently in a 31.5 percent drawdown that had lasted for
28 months. The same numbers for the NASDAQ 100 were a 302 percent increase
and a 77.5 percent drawdown that had lasted for 25 months.
We really don’t need to know why there are such differences in the behavior
between the different stocks making up the indexes. It doesn’t take much, however, to understand that the calmer behavior of the Dow is because it’s made up of
older, larger, old-economy companies that are not as sensitive to the psychologic
twists and turns of the general market as are the younger, new-technology, and
high interest rate–sensitive companies of the NASDAQ 100. Be that as it may, all
we need to acknowledge is that differences are present and we should come up
with a system that works, on average, equally as well on all markets.
As the systems were featured in Active Trader magazine, they included the
results from using dynamic ratio money management (DRMM), which basically
means that all markets will benefit from the results from all other markets, resulting in a faster equity growth, a smoother equity curve, and more often than not,
lower drawdowns. The new results from the initial research do not depend on
DRMM. Instead, they include only the normalized results from investing $100,000
per trade.
Looking at the buy-and-hold performance numbers for the Dow and NASDAQ
100, we can calculate the average annual return for the two indexes to 7.5 percent
per year [((206 /100)^(1/10) 1) * 100] and 11.7 percent per year [((302
PART 2
86
/100)^(1/10) 1) * 100], respectively. Now, knowing that both markets currently are
in rather severe drawdowns, we understand that the good years normally are much
better than that, but this is what we can expect the long-term growth of a well-diversified buy-and-hold type portfolio to be, given the last 10 years of market data.
As systems traders, naturally we would like to beat that. But beating the actual return numbers isn’t the only thing we like to do. We also would like to do it
while spending less time in the market, avoiding any 77 percent drawdowns and
generally increasing our wealth at a calmer and steadier pace than the buy-andhold strategy. That is, we would like to keep the volatility down to a minimum,
given our desired return on the capital. But sometimes we also need to go the other
way around, and lower our expectations regarding the final return in favor of the
steady but slower equity growth. All this will make sense in Part 4. But to get
there, we first need to come up with a set of systems that work, on average, well
on as many types of markets as possible.
EXPORT CODE
{1}{Individual market export, with Normalize(True). Set ExportSwitch(True).}
Variable: ExportSwitch(True);
If ExportSwitch = True Then Begin
Variables:
StartPeriod(0), EndPeriod(0), PeriodLength(0), TradeType(""),
NameLength(0), FileString(""), TestString(""), NoTrades(0),
SetExportArray(0), TradeCounter(0), SumProfit(0), MaxProfit(0),
DrawDown(0), MaxDrawDown(0), DDPercent(0), MaxDDPercent(0),
WinningTrades(0), SumTrLen(0), ExportArrayPos(0), PercentInTrade(0),
AverageProfit(0), AverageTrLen(0), SumSquareProfit(0),
StDevProfit(0), RiskRatio(0), PercentWinners(0), ProfitFactor(0),
LosingTrades(0), RiskFactor(0);
{2} Arrays:
TradeProfit[1000](0), TradeLength[1000](0);
{3} If BarNumber = 1 Then Begin
StartPeriod = DateToJulian(Date);
If AllowLong = True Then
TradeType = "Long";
If AllowShort = True Then
TradeType = "Short";
If AllowLong = True and AllowShort = True Then
TradeType = "Both";
87
NameLength = StrLen(GetStrategyName) - 6;
FileString = "D:\BookFiles\InitTest-" +
RightStr(GetStrategyName, NameLength) + "-" +
RightStr(NumToStr(CurrentDate, 0), 4) + ".csv";
TestString = "Market" + "," + "Direction" + "," + "Trades" + "," +
"PercWin" + "," + "NetProfit" + "," + "AvgProfit" + "," +
"StDevProfit" + "," + "RiskRatio" + "," + "ProfitFactor" + "," +
"RiskFactor" + "," + "MaxDD" + "," + "PercDD" + "," +
"PercTime" + "," + "AvgLength" + NewLine;
FileAppend(FileString, TestString);
End;
{4} NoTrades = TotalTrades;
If NoTrades > NoTrades[1] Then Begin
TradeProfit[SetExportArray] = PositionProfit(1);
TradeLength[SetExportArray] = DateToJulian(ExitDate(1)) DateToJulian(EntryDate(1)) + 1;
SetExportArray = SetExportArray + 1;
End;
{5} If LastBarOnChart Then Begin
{Alt: If LastCalcDate = Date + 1 Then Begin}
EndPeriod = DateToJulian(Date);
PeriodLength = EndPeriod - StartPeriod;
For ExportArrayPos = 0 To (NoTrades - 1) Begin
SumProfit = SumProfit + TradeProfit[ExportArrayPos];
If SumProfit > MaxProfit Then
MaxProfit = SumProfit;
DrawDown = MaxProfit - SumProfit;
If MaxProfit > 0 Then
DDPercent = DrawDown * 100 / (100000 + MaxProfit)
Else
DDPercent = DrawDown * 100 / 100000;
If DrawDown > MaxDrawDown Then
MaxDrawDown = DrawDown;
If DDPercent > MaxDDPercent Then
MaxDDPercent = DDPercent;
If TradeProfit[ExportArrayPos] > 0 Then
WinningTrades = WinningTrades + 1;
PART 2
88
SumTrLen = SumTrLen + TradeLength[ExportArrayPos];
End;
{6} If PeriodLength <> 0 Then
PercentInTrade = SumTrLen * 100 / PeriodLength
Else
PercentInTrade = 0;
If NoTrades <> 0 Then Begin
AverageProfit = SumProfit / NoTrades;
AverageTrLen = SumTrLen / NoTrades;
PercentWinners = WinningTrades * 100 / NoTrades;
End
Else Begin
AverageProfit = 0;
AverageTrLen = 0;
PercentWinners = 0;
End;
{7} For ExportArrayPos = 0 To (NoTrades - 1) Begin
SumSquareProfit = SumSquareProfit +
Square(TradeProfit[ExportArrayPos]);
End;
{8} If NoTrades <> 0 Then
StDevProfit = SquareRoot((NoTrades * SumSquareProfit Square(NetProfit)) / (NoTrades * (NoTrades - 1)))
Else
StDevProfit = 0;
If StDevProfit <> 0 Then
RiskRatio = AverageProfit / StDevProfit
Else
RiskRatio = 0;
{9} If GrossLoss <> 0 Then Begin
ProfitFactor = GrossProfit / -GrossLoss;
LosingTrades = NoTrades - WinningTrades;
If LosingTrades <> 0 and NoTrades <> 0 Then
RiskFactor = NetProfit / ((-GrossLoss / LosingTrades) * NoTrades)
Else
RiskFactor = 0;
89
End
Else Begin
ProfitFactor = 0;
RiskFactor = 0;
End;
TestString = LeftStr(GetSymbolName, 5) + "," + TradeType + "," +
NumToStr(NoTrades, 0) + "," + NumToStr(PercentWinners, 2) + "," +
NumToStr(NetProfit, 2) + "," + NumToStr(AverageProfit, 2) + "," +
NumToStr(StDevProfit, 2) + "," + NumToStr(RiskRatio, 2) + "," +
NumToStr(ProfitFactor, 2) + "," + NumToStr(RiskFactor, 2) + "," +
NumToStr(MaxDrawDown, 2) + "," +
NumToStr(MaxDDPercent, 2) + "," +
NumToStr(PercentInTrade, 2) + "," +
NumToStr(AverageTrLen, 2) + NewLine;
{10} FileAppend(FileString, TestString);
End;
End;
COMMENTS ON THE CODE
Let’s go through the code step-by-step to see how it works:
1.
2.
3.
The variable ExportSwitch(True) must be placed on top of the code or even
as an Input. The other variables only become active when ExportSwitch is set
to True. To speed up the computing time, the program will not run through
the rest of the code, when ExportSwitch is set to False.
We need to create two arrays to contain the data for our calculations. We
could have done without the arrays and instead run through all the calculations for each bar, but to speed up the computing time, we will do most of
the calculations only once, on the very last bar on the chart. The arrays are
now set to hold 1,000 trades each. The larger the arrays, the slower the calculations, so you might want to change this number to what makes the most
sense for the system you currently are working on.
These calculations and exports only need to be done once, on the very first
bar on the chart. By altering the state of the variables AllowLong and
AllowShort at the very top of the code (see the code for any of the individual systems), we can test all long and short trades, either separately or together. Then we create the file that we will import into Excel (variable
FileString), and the column headers for the data we need to export later (variable TestString).
PART 2
90
4.
5.
6.
7.
8.
9.
These calculations are done on every bar on the chart. We are now filling the
array TradeProfit with the result of each trade. An array is a series of values
stored in a specific order. In this case, the first position in the array will hold
the result of the first trade, and so on. The second array, TradeLength, is
filled with data regarding the length of the trade. Each array can store 1,000
trades, as specified under step two.
All remaining calculations will only be executed on the very last bar on the
chart. Note: If you plan to use this code and use the criteria Open Next Bar
(or Open Tomorrow) for your entries and exits, you need to use the alternative function. The first thing we need to do is to run a loop (that starts with
the word “For”) to calculate the total profit (variable SumProfit) by adding
all the values contained in the array TradeProfit. Take note of all new equity
highs (variable MaxProfit): From these, we can calculate the maximum
drawdown (variables DrawDown, MaxDrawDown, DDRatio, and
MaxDDRatio). We also count the number of winning trades (variable
WinningTrades) and sum up the length of all trades in the variable
SumTrLen, using the data from the array TradeLength.
Moving out of the first loop, we now can calculate the variables
PercentInTrade, AverageProfit, AverageTrLen, and PercentWinners, which
all should be self-explanatory.
The second loop (also starting with the word “For”) sums up the squared
profits from all trades in the SumSquareProfit variable.
Moving out of the second loop, we can go on and calculate the standard deviation of all trades (variable StDevProfit), and the ratio between the average
trade and the standard deviation of all trades (variable RiskRatio). The variable RiskRatio measures the risk of the system by comparing the average
trade with the dispersion of all trades (the standard deviation). The higher the
value of the average trade and the less dispersed all the individual trades, the
more sure you can be regarding the outcome of each individual trade, and,
consequently, the less risky the system.
The calculation for the variable LosingTrades should be self-explanatory.
The variable ProfitFactor stores the relation between every dollar earned and
every dollar lost, calculated as the gross profit, divided by the gross loss.
Obviously, if the gross profit from all winning trades is larger than the gross
loss from all losing trades, the variable ProfitFactor will be greater than 1,
which is a must for a profitable system. The variable RiskFactor calculates
the relationship between the final (net) profit and every dollar risked, which
is not the same as every dollar lost. To calculate the dollars risked, the system must have a stop-loss level. To calculate the dollars risked for all trades,
first divide the gross loss by the number of losing trades, to get a value for
the average losing trade. Second, assuming the dollars lost in the average losing trade also represent the value we were willing to risk and lose in each and
91
every trade (this is not always the case and depends on a few assumptions,
but will do as a good approximation), multiply the dollars lost in the average
losing trade by the total number of trades to arrive at the total value the system risked throughout all trades over the entire test period. Third, divide the
net profit by this value to arrive at the RiskFactor.
10. The file export takes place in the command FileAppend. The name of the file
is specified by the variable FileString, created in step three.
THE EXPORTED DATA
Once you’ve exported all the necessary data for all markets to be analyzed together, you can open the newly created file in Excel for further analysis. Figure 7.1
shows what this may look like after the data have been sorted on the ticker symbol for each market.
If you compare all column headers in Figure 7.1 with the lowest part of the
TradeStation export function, you will see that each variable is exported to its own
column in the same way for all markets tested. For example, the value in cell G3
tells us that the average profit per trade for Altera (ALTR) is $1,847.63, whereas
cell L9 tells us that the worst drawdown, measured in percentage terms, for
Citicorp is 9.91 percent. Arranging the statistics in this way makes it is easy to
rank and compare all the markets with each other by simply using the sort buttons
on the Excel toolbar. Note that the percent drawdown is allowed to surpass 100
percent in this table.
However, to find out how reliable and robust a system is when traded on several markets and during various market conditions, we also need to summarize the
results from all markets in one easy to understand table. Figure 7.2 shows what such
a table may look like when placed directly under the exported data for all the markets.
Because we will work extensively with this table over the next several pages,
let’s take the time to step through it, to make sure we understand how to calculate
all the values and how to interpret their meanings.
Cell H68 shows how many markets were profitable. The value 81.54 is calculated using the formula =COUNTIF(E$2:E66,">0")*100/COUNT(E$2:E66),
FIGURE
7.1
Excel file showing sorted data.
PART 2
92
FIGURE
7. 2
Summary table showing market results.
where column E refers to the net profit for all markets. The dollar mark inside the
cell reference E$2 makes the formula adjust automatically to the number of markets tested. This makes it easy to copy and paste tables between spreadsheets,
instead of having to create a new table for every new spreadsheet.
Cell C70 shows the average number of trades for each market. The value
50.20 is calculated using the formula AVERAGE(C$2:C66), in which column C
refers to the number of trades produced by each market.
Cell C71 shows the standard deviation of the number of trades produced. The
value 11.73 is calculated using the formula STDEV(C$2:C66). It indicates that
68 percent of all trading sequences will produce somewhere between 38.47 (50.20
11.73) to 61.93 (50.20 11.73) trades, which is further indicated by cells C72
(C70 C71) and C73 (C70 C71).
The formulas for cells D70 to F73 are the same as those used in cells C70 to
C73, except that the calculations are based on the data in columns D to F.
If you ask me, I think a high number of profitable markets (cell H68) is way
more important than a high number of profitable trades (cell D70). You shouldn’t
care so much about the outcome of the very next trade, as long as you know you
will end up on top if you do what you should over a longer sequence of trades. A
psychiatrist specializing in “treating” traders once told me that he wished all
traders could learn to focus on the trading procedure over a specified time period
instead of the event (trade) at hand. Then, all traders would have a much easier
time cutting their losses, because letting a losing or slow trade run only makes it
more difficult to reach the true goal—to produce a profit at month’s end instead
of with every single trade. From this it also follows that a high number of prof-
93
itable months is more important than a high number of profitable trades, and
sometimes it might be a good idea to take a higher number of losing trades to
increase the number of profitable months. This is especially true when we need to
free up capital from trades that are going nowhere.
Sometimes, when testing the same system on several markets, or the same
market with several systems, the average net profit from all trading sequences (cell
E70) can be negative despite a positive average profit per trade (cell F70), or vice
versa. Because the number of trades can vary within each trading sequence, a trading sequence with a high number of relatively small losses will weigh down the
average net profit relatively more than the average profit per trade. A trading
sequence with a low number of relatively large winners, on the other hand, will
increase the value of the average profit per trade relatively more than the average
net profit.
However, because we don’t know if a market that produced relatively few or
many trades over the testing period will continue to do so in the future, we cannot
place any significance on the net profit produced by that market. All we can do is
use the average profit per trade, regardless of how many trades it is based on, as
one of many estimates for the average profit per trade for all markets. We use the
average of all averages from all markets as an estimate for the true, but always
unknown, average profit per trade.
Another way to look at it is to assume that each market is producing approximately the same number of trades, no matter how many trades there are behind a
certain average profit per trade for a certain market. In that case, a positive (negative) average profit per trade will also produce a positive (negative) average net
profit per market. This is also more in line with what we can expect in real-life trading. One error we deliberately make during this stage of the testing is to equalize
one trading sequence with trading one market over a longer period of time (say 10
years). In real life, one trading sequence is instead equal to trading several markets
(10, for example) over a shorter period of time (say one year). In this case, different markets will produce a varying number of trades over different periods, but the
number of trades over all trading sequences (in this case defined by units of time,
rather than specific markets) is more likely to stay approximately the same.
Cell G71 shows the average standard deviation for the profit per trade produced by each market. The value, 8,337.05, is calculated using the formula
AVERAGE(G$2:G66), where column G refers to the standard deviation of profits produced by each market. It indicates that 68 percent of all trades within one
trading sequence will result in a profit ranging from $7,042.01 (1,295.04 8,337.05) to $9,632.09 (1,295.04 8,337.05), which is further indicated by cells
G72 ( F70 G71) and G73 ( F70 G71).
Note that the values in cells G71 to G73 are much larger (positive or negative) that those in cells F71 to F73. This is because the values in cells G71 to G73
give an indication of how much the results per trade can vary within one market,
94
PART 2
or one trading sequence, whereas cells F71 to F73 indicate how much the average
profit per trade is likely to vary over several markets or several trading sequences.
It only makes sense that the average profit per trade is likely to vary less than the
actual profit per trade, just as, for example, a moving average of prices fluctuates
less than the price itself. Normally, the values in cells F71 to F73 are of greater
interest than those in cells G71 to G73.
Cell H71 shows the average risk-adjusted return for one market or trading
sequence. The value 0.15 is calculated using the formula AVERAGE(H$2:H66),
where column H refers to the risk ratio as calculated with the TradeStation export
function. The value in column H also could have been calculated using the values
from columns F and G, so that the value in cell Hn would equal Fn / Gn.
Cell H73 shows the risk-adjusted return over several markets or trading
sequences. The value 0.96 is calculated using the formula F70/F71. Note that the
value in cell H73 is much higher than that in cell H71. This is because in cell H73,
we’re using the standard deviation of the average profit per trade from several markets, as opposed to the standard deviation of the profit per trade from individual
markets, as in cell H71. Because the standard deviation of the average profit per
trade is less than the standard deviation of the outcome of all individual trades, the
risk-adjusted return will be greater over several markets or trading sequences than
over one single market or sequence given that the returns are similar from all markets. The value in cell H73 is of greatest interest to us.
The calculations and values in cells C75 to H78 should be pretty much selfexplanatory. The most important cells or values to consider in the bottom half of the
table are the average profit and risk factors and their respective standard deviations.
An average profit factor above one means that the system tested profitably enough
on the profitable markets to make up for the losses made in the losing markets. The
same goes for a risk factor above zero. One way to get a dollars-and-cents feel for
the risk factor is to equal its value to dollars made per dollar risked. In the case of
Figure 7.2, a value of 0.28 indicates that the system is likely to make 28 cents per
dollar risked. Note, however, that if the standard deviation for the risk factor is higher than the risk factor itself, a number of trading sequences will lose money. In this
case, a value of 0.29 in cell D76 indicates that 68 percent of all trading sequences
will produce a profit per dollar risked ranging from 1 cent to 57 cents.
As already mentioned in the beginning of this section, the trade length and
time spent in the market variables are important in that we need to balance these
numbers against the number of markets we would like to trade and the nature of
the trading strategy. Aside from that, because this is a book about relatively shortterm trading strategies, we will try to keep the average trade length down to
approximately five to ten days. Finally, at this point of the analysis work, we won’t
care so much about the drawdown values. As mentioned in Chapter 5, the drawdown is not a core system characteristic and is more efficiently dealt with via
mathematical expectancy and the probability for a winning trade.
95
INITIAL DESCRIPTION OF THE SYSTEMS
Before we look at the individual systems, I would like to point out that all original
systems are completely unoptimized, and the little optimization or tweaking I
indulged in doesn’t take us too far away from the type of reasoning I used when I
put the systems together in the first place.
When it comes to finding an entry technique, I am not all that interested in
finding the most optimal parameter settings. What is more important is to find settings that make sense to me and that I can live with because I understand why they
are as they are. In fact, the better you know and understand the system, the less
optimizing you need to do, at least when it comes to the entry techniques.
However, I do like to optimize the stops and the exits, but that will wait until
Part 3. For now, we will keep most of the exits in the systems as they were presented originally. If you read through this part and still are interested in finding the
most optimal parameters for the entry, you can use the techniques given in Part 3
to optimize the exits.
The original results also are presented as they were in ATM, which means
that sometimes the terminology is different from that used in the rest of the book.
For example, for the hybrid system No. 1 and the RS system No. 1, I use the term
risk–reward ratio as a ratio between the final net profit and the maximum historical drawdown. This is not a correct use of this term, and in the rest of the book,
the risk–reward ratio refers to the average profit per trade divided by the standard
deviation of all trades.
For the Harris 3L-R pattern variation system, I also use the term profit–loss
ratio. Throughout the rest of the book, this term is replaced by the (initial)
risk–reward relationship, which refers to the distances between the entry price, the
stop loss, and profit target (or final profit) when entering into a trade. The
risk–reward relationship is expressed as the profit target in relation to the stop loss,
as in “2:1,” which means that the profit target is placed twice as far from the entry
point as the stop loss. OK, let’s get to it.
CHAPTER
8
Hybrid System No. 1
O
riginally presented in September 2000, this is a short-term hybrid system that
falls somewhere between a bottom-picking strategy and a trend-following breakout strategy. The system waits for a retracement to occur, then enters when the
market reverses by an amount equal to half the retracement. For example, if a
stock rallied to a new high at 80, then retraced to 70, the system would go long
when the stock moved back above 75 (halfway between the high and the retracement low).
As a bottom-picking strategy, it requires that the bottom be confirmed by a
move retracing half the previous decline. As a breakout system, it tries to anticipate the breakout by going long at the halfway point between the most recent highs
and lows.
SUGGESTED MARKETS
Stocks, stock index futures, and index shares (SPDRs, DIAs, QQQs).
ORIGINAL RULES
Enter long with a stop order after the market has made a nine-day low and then
retraced half the move from that low to the highest high of the last nine days.
Risk 0.5 percent of the available equity per trade. At the time of entry, calculate the number of stocks per trade as 0.005 multiplied by available equity,
divided by the dollar value of the distance between the entry price and the lowest
low of the last nine days.
97
PART 2
98
Exit with a trailing stop if the market falls below the lowest low of the last
nine days.
Exit with a loss if the market is below the entry price after nine days.
TEST PERIOD
January 1, 1990 to July 12, 2000.
TEST DATA
Daily stock prices for the 25 most-traded stocks on the NASDAQ 100 list, excluding those stocks that also can be found in other indexes, such as Microsoft and
Intel in the Dow Jones Industrial Average and S&P 500 index.
STARTING EQUITY
$100,000 (nominal).
SYSTEM PROS AND CONS
The long-only trend-following nature of the system makes it vulnerable to market
corrections, which explains the rather extensive drawdowns over the last few
months (not shown). This system would probably benefit from the addition of a
trend filter (such as a long-term moving average) that would only allow trades in
the direction of the prevailing trend.
Other enhancements include only trading those stocks that show the highest
relative strength compared to the market as a whole (i.e., the underlying index), or
including some sort of volume confirmation, such as an increasing on balance volume (OBV) value.
Although this system does better than buy-and-hold for both the Dow and
S&P 500, it doesn’t manage to keep up with the NASDAQ 100. Note, however,
that the system only risks 0.5 percent of available equity per trade, which translates into a risk–reward ratio of 21.8 (in this case, calculated as total return divided by max drawdown). For a buy-and-hold strategy for the NASDAQ 100, the
same ratio is 40.9. However, a buy-and-hold strategy is in the market all the time,
which also adds to the risk, albeit on a more subjective level.
Risking 1 percent per trade produced a return and drawdown of 1,514 percent and 52.89 percent, respectively, for a risk–reward ratio of 28.6 (1,514 / 52.89).
(Note that in some of the original system texts, I defined the risk–reward ratio as
the net profit divided by the largest drawdown. This is not the best or correct definition, but only an easy and commonly used way to get a first feel for the system
compared to other systems.) This is still not as good as a buy-and-hold, but some
CHAPTER 8
Hybrid System No. 1
99
of the 25 stocks in the test portfolio were not listed until very recently (such as
Amazon.com, which didn’t start contributing to the portfolio equity until August
1997). During the first year of trading, only 14 of our 25 stocks were tradable.
REVISING THE RESEARCH AND MODIFYING THE SYSTEM
Because the original testing showed some very good results, I had high hopes
that so would this second run of testing on more markets and fresher data. Table
8.1 shows that I had no reason to be disappointed, with as many as 91 percent of
all tested markets delivering a profit. The average profit per trade came out to
$1,048 and the profit and risk factors to 1.39 and 0.24, respectively. The most
important standard deviation numbers also are very low, which among other
things, results in a very good risk–reward ratio of 0.91 (1,049 / 1,149—the average profit per trade divided by its standard deviation, a more correct definition
of the risk–reward ratio). The only negative is the average trade length at 20 days
and the average time spent in the market, which both are a little too high for the
system to be considered short term. Therefore, I tried to modify the rules a bit
to make it more short term, hopefully, without losing any or as little performance as possible.
The first thing I did was to shorten the slow-trade stop to four days, but that
did not change the performance or the system characteristics all that much, which
gave a first indication that the slow-trade stop might not be needed at all. With the
slow-trade stop at its original nine-day setting, I changed the retrace period
between the most recent high and low prices to six days, expecting a larger num-
TAB LE
8.1
Retesting the Original Hybrid System I
Original system, long only
PercProf: 90.77
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
140.83
34.87
34.38
4.35
122,904.33
105,868.56
1,048.92
1,149.15
10,311.97
Market
0.09
High:
Low:
175.70
105.96
38.73
30.04
228,772.90
17,035.77
2,198.07
(100.22)
11,360.89
(9,263.04)
Portfolio
0.91
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.39
0.24
82,151.19
39.37
69.44
20.47
St. Dev:
0.41
0.24
42,524.99
20.80
6.35
2.62
High:
Low:
1.80
0.98
0.49
0.00
124,676.17
39,626.20
60.17
18.57
75.80
63.09
23.09
17.86
PART 2
100
ber of shorter trades, but also an increasing number of losing trades, which would
deteriorate performance somewhat.
As it turned out, Table 8.2 shows that the average trade length did decrease
from 20 days to 15 days, but surprisingly, the percentage of winning trades also
increased to 36 percent, increasing the average net profit to $141,896, despite a
slightly lowered average profit per trade. The profit and risk factors also increased
a little, but what is more important is that all the important standard deviation numbers decreased, indicating that the system actually became more reliable.
Of course, these surprisingly positive results prompted a test with an even
shorter retrace period of three days. However, this did not better the results enough
to warrant an even shorter retrace period. Note that I did not test any other retrace
periods than those mentioned. It might be that other retrace periods, surrounding
those tested, might work better.
With the retrace period back at six days, the next step was to once again test
various values for the slow-trade stop. But with the slow-trade stop set to six days,
results did not improve enough, if at all, as Table 8.3 shows. In fact, with a shorter slow-trade stop only decreasing performance, it is clear that it can be removed
completely, as it has in Table 8.4, which shows that the aggressive level for the
entry also has been increased to a factor of three, meaning the entry will now take
place after only a third of the distance between the lowest low and highest high has
been taken back.
Table 8.4 shows the results for a system based on a six-day retrace period, no
slow-trade stop, and a one-third retracement of the highest-high to lowest-low distance to trigger an entry. It shows that the results continued to improve the more
TAB LE
8.2
Revised Performance Results, with Six-day Retrace Period
Long only: six-day retrace period
PercProf: 90.77
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
187.55
49.77
36.08
5.33
141,896.16
119,300.04
915.26
958.46
8,510.40
Market
0.10
High:
Low:
237.32
137.78
41.41
30.74
261,196.20
22,596.12
1,873.72
(43.20)
9,425.66
(7,595.14)
Portfolio
0.95
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.42
0.25
77,839.56
36.55
68.97
15.35
St. Dev:
High:
0.49
1.91
0.25
0.50
42,152.75
119,992.31
23.87
60.42
6.06
75.02
2.10
17.45
Low:
0.93
(0.00)
35,686.81
12.68
62.91
13.25
CHAPTER 8
Hybrid System No. 1
TAB LE
101
8.3
Slow-trade Stop at Six Days
Long only: six-day retrace period, six-day slow-trade stop PercProf: 89.06
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
195.73
50.16
34.76
5.60
139,303.16
117,466.37
857.00
923.85
8,300.17
Market
0.10
High:
Low:
245.90
145.57
40.36
29.16
256,769.53
21,836.79
1,780.85
(66.85)
9,157.17
(7,443.17)
Portfolio
0.93
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.41
0.50
1.91
0.92
0.25
0.25
0.50
(0.00)
78,570.71
42,015.00
120,585.70
36,555.71
36.12
21.56
57.69
14.56
67.56
5.96
73.52
61.59
14.35
1.90
16.26
12.45
Average:
St. Dev:
High:
Low:
aggressive the system. The most important thing to notice is a risk–reward ratio
for the entire portfolio above one, which means that at least 84 percent (68 32
/ 2) of all trading sequences now have or should have a positive average profit per
trade. This is further confirmed by a positive value for the lower one standard deviation boundary for the risk factor. The profit factor is also at its highest so far at
1.44. I settled for this version of the system before I decided to test both the long
and the short side simultaneously.
TAB LE
8.4
Removing Slow-trade Stops
Long only: six-day retrace period,
no slow-trade stop, aggressive level three
PercProf: 96.88
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
212.14
59.42
33.42
4.82
162,892.09
109,794.45
923.64
872.67
8,423.52
Market
0.10
High:
Low:
271.56
152.72
38.24
28.60
272,686.55
53,097.64
1,796.31
50.97
9,347.16
(7,499.88)
Portfolio
1.06
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.44
0.28
77,309.40
34.52
71.87
14.30
St. Dev:
High:
0.48
1.93
0.25
0.53
40,877.93
118,187.32
19.05
53.56
5.04
76.91
2.62
16.92
Low:
0.96
0.02
36,431.47
15.47
66.83
11.68
PART 2
102
FIGURE
8.1
NASDAQ 100 index traded using Hybrid System I.
Unfortunately, the short side did not produce good enough results to warrant
trading without any other types of adjustments, such as the addition of a trend filter or relative-strength filter. Nonetheless, we will take this version of the system
with us to Part 3 where we will try to substitute the stops and make the system
more short term. We will also look at how the system will operate with a trend or
relative-strength filter, in an effort to decrease the percentage of time spent in the
market. Figure 8.1 shows a few sample trades in the NASDAQ 100 index, generated with this latest version of the system.
TRADESTATION CODE
Variables:
AllowLong(True), AllowShort(False), RetracePeriod(6), Aggressiveness(3),
CHAPTER 8
Hybrid System No. 1
103
RetraceDistance(0), LongEntryLevel(0), ShortEntryLevel(0);
{Code for normalizing the number of contracts traded goes here.}
RetraceDistance = (Highest(High, RetracePeriod) - Lowest(Low, RetracePeriod)) /
Aggressiveness;
LongEntryLevel = Lowest(Low, RetracePeriod) + RetraceDistance;
ShortEntryLevel = Highest(High, RetracePeriod) - RetraceDistance;
If MarketPosition = 0 Then Begin
If AllowLong = True and Close < LongEntryLevel Then
Buy ("L-Sep 00") NumCont Contracts Next Bar on LongEntryLevel Stop;
If AllowShort = True and Close > ShortEntryLevel Then
Sell ("S-Sep 00") NumCont Contracts Next Bar on ShortEntryLevel Stop;
End;
If EntryPrice > 0 Then Begin
ExitLong ("L-Stop") Next Bar at Lowest(Low, RetracePeriod) Stop;
ExitShort ("S-Stop") Next Bar at Highest(High, RetracePeriod) Stop;
End;
{Code for testing stops in Excel goes here (see Part 3 of book), with
Normalize(False). Set SurfaceChartTest(True). Disable original stops in system.}
{Code for initial market export goes here, with Normalize(True). Set
ExportSwitch(True).}
{Code for testing robustness goes here (see Part 3 of book), with Normalize(True).
Set RobustnessSwitch(True).}
{Code for exporting results for money management analysis goes here (see Part 4
of book), with Normalize(False). Set MoneyExport(True).}
CHAPTER
9
RS System No. 1
Originally presented in October 2000, this is a short-term relative strength (RS)
system that compares the stock price with its underlying market index, but also
looks for confirmation from volume. The first step is to calculate the relative
strength of the stock compared to the market as a whole, then take the percentage
difference between the relative strength curve and its five-day moving average. A
value above one (the higher the better) indicates the stock has moved stronger than
the market as a whole.
The second step is to calculate the percentage difference between the onbalance-volume indicator and its five-day moving average. A value above one (the
higher the better) indicates the volume fueling the move is above its five-day
moving average and that the market has a short-term interest in the stock.
The final step is to multiply both the percentage differences to create a
volume-weighted relative-strength curve. A value above one (the higher the better)
indicates that the market has a short-term interest in the stock, but also that it is
doing better than average in terms of the overall market. (Or, if the interest is low,
the stock is still moving strongly enough to warrant a trade, and vice versa.)
SUGGESTED MARKETS
ORIGINAL RULES
Enter long at the close when the volume-weighted relative-strength curve crosses
above one.
105
PART 2
106
Risk 0.5 percent of available equity per trade. At the time of entry, calculate
the number of shares to buy as 0.005 multiplied by available equity, divided by the
dollar value of the distance between the entry price and the stop loss.
Exit at the close when the volume-weighted relative-strength curve crosses
below one.
Exit with a loss if the market falls below the entry price minus 4 percent.
TEST PERIOD
December 11, 1985 to July 12, 2000.
TEST DATA
Daily stock prices for the 30 most actively traded NASDAQ 100 stocks, excluding
those stocks that also can be found in other indexes, such as Microsoft and Intel in
the Dow Jones Industrial Average and S&P 500 index. The amount of $20 per
trade has been deducted for slippage and commission.
STARTING EQUITY
$100,000 (nominal).
This is a long-only system, which makes it vulnerable to market conditions. The
system probably would benefit from the addition of a trend filter (such as a longterm moving average) that would only allow trades in the direction of the prevailing trend. Developing a similar strategy for the short side would make it possible
to make money no matter what direction the market is heading.
Although this system does better than buy-and-hold for both the Dow and
S&P 500, at first glance it doesn’t quite seem to keep up with the NASDAQ 100.
However, looking closer at the numbers reveals that the risk–reward ratio (in this
case, total return divided by maximum drawdown) for a buy-and-hold strategy for
the NASDAQ 100 comes out to 68.6. For this system, only risking 0.5 percent of
available equity per trade, the same number comes out to 80.8, which is a clear
indication that it allows you to make more money while risking less.
Another favorable aspect of the system is that a buy-and-hold strategy is
always in the market, risking 100 percent of available equity. While being in the
market all the time might not add to the risk, it sure adds to the agony. Finally,
some of the 30 stocks in the test portfolio were not listed until very recently (such
as Amazon.com, which didn’t start contributing to the portfolio equity until
August 1997).
CHAPTER 9
RS System No. 1
107
Table 9.1 shows the results produced by the original system. This is a pretty good
start, showing a high percentage of profitable trading sequences and a decent profit factor. The average profit per trade is, however, a little too low. If we can increase
the average profit per trade, we also should be able to increase the profit and risk
factors. Hopefully, this can be done while also increasing the risk–return ratio, currently at 0.60.
Because this is a relative-strength system that we later will try to use as a filter for the other short-term systems, we will start by trying to increase the average
trade length by getting rid of the stop loss. If the results change for the better or
remain relatively stable, the stop loss fulfilled little purpose anyway, and the fewer
rules we can get by with, the better off we are. Table 9.2 shows that this actually
improved results quite a bit. The average profit increased to $229.77, while the
profit and risk factors increased to 1.14 and 0.08, respectively. The risk–reward
ratio also increased, which indicates the system produces more homogeneous and
similar-looking trades. However, for a trend filter, the trading horizon is still a little short at 6.18 days, on average.
Let’s keep testing the system without the stop loss, but try to come up with a
way to lengthen the number of days in a trade, while decreasing the time spent in
the market. To do this, the number of trades must be decreased; you could work
with a longer lookback period for the relative strength calculation. Table 9.3 shows
the result for a version of the system with a 20-day relative strength lookback. It
contains both good and bad news. The good news is that the average profit per
trade increased together with the profit and risk factors. The average trade length
TAB LE
9.1
Retesting of RS System No. 1
PercProf: 70.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
405.60
74.91
38.64
3.86
53,487.76
90,677.39
155.09
257.41
4,865.10
Market
0.03
High:
Low:
480.51
330.69
42.50
34.78
144,165.15
(37,189.63)
412.50
(102.31)
5,020.19
(4,710.00)
Portfolio
0.60
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.09
0.06
98,225.82
53.55
56.61
5.68
St. Dev:
High:
0.15
1.25
0.09
0.15
49,403.31
147,629.13
30.82
84.37
3.43
60.04
0.38
6.06
Low:
0.94
(0.04)
48,822.50
22.73
53.19
5.31
PART 2
108
TAB LE
9.2
Removing the Stop Loss
Long only: No stop loss
PercProf: 80.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
405.55
74.96
40.39
3.55
82,811.65
98,064.36
229.77
278.19
5,130.55
Market
0.04
High:
Low:
480.51
330.59
43.95
36.84
180,876.01
(15,252.70)
507.96
(48.42)
5,360.32
(4,900.78)
Portfolio
0.83
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.14
0.16
1.30
0.98
0.08
0.10
0.18
(0.01)
94,117.39
50,003.95
144,121.34
44,113.43
48.08
26.36
74.44
21.73
61.53
1.65
63.18
59.89
6.18
0.37
6.55
5.81
Average:
St. Dev:
High:
Low:
also increased to about 13 days. The bad news is that risk–return ratio decreased a
little, as did the number of profitable markets.
Increasing the lookback even further, to 50 days, continued to increase the
average profit and the profit and risk factors. The risk–return ratio also increased
somewhat, but not enough to take us back to what we had in Table 9.2. This tells
us that increasing the lookback period is not the best way to go. Another way to
make the average trade length longer is to make it easier for an individual stock to
TAB LE
9.3
Twenty-day Relative Strength Lookback
Long only: No stop loss, 20-day lookback
PercProf: 75.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
184.30
40.05
36.86
5.01
114,309.41
144,384.69
761.90
1,048.93
8,696.44
Market
0.07
High:
Low:
224.35
144.25
41.87
31.86
258,694.10
(30,075.27)
1,810.84
(287.03)
9,458.34
(7,934.53)
Portfolio
0.73
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.33
0.20
80,636.09
44.10
58.36
13.07
St. Dev:
High:
0.40
1.73
0.24
0.44
38,344.13
118,980.21
28.01
72.11
3.53
61.89
1.73
14.80
Low:
0.93
(0.04)
42,291.96
16.09
54.82
11.34
CHAPTER 9
RS System No. 1
109
enter into a trade. Unfortunately, however, most likely this will also increase the
time spent in the market and the number of markets being in a trade at once.
Table 9.4 shows what happened when the required strength was lowered to
0.95 (as opposed to the original strength of one), meaning the relative-strength and
volume conditions for entering have been relaxed quite a bit. Thus, either one of
the original conditions doesn’t have to be completely fulfilled. This did improve
performance quite a bit. The average profit per trade came out to $1,300, with the
risk–reward ratio at 0.93, which is very good. These good numbers also found confirmation from high profit and risk factors, which both have their lower standard
deviation boundaries above one and zero, respectively. The average trade length
came out close to 20 days, which is what we’re looking for. The only negative is
the high percentage of time spent in the market. Over 70 percent is a little too
much, but because this system will primarily be used as a filter for other systems,
we will live with this number.
It seems that decreasing the required strength for the entry even further
would continue to improve on the results. However, decreasing the required
strength too much soon will result in a system that keeps us in a trade in all markets all the time, and the purpose behind the system will be lost. Therefore, I will
not experiment with this number any further, but only conclude that a system with
a 20-day lookback period and a required strength of 0.95 produces the types of
trades we’re interested in, and I’ll settle for this version.
Repeating the research, trading both the short and the long side of the market, did not produce good results at all. Therefore, for now, this system will remain
long only. Perhaps the short side still can work as a filter for other systems trading
TAB LE
9.4
Lowered Relative Strength
Long only: No stop loss, 20-day lookback,
strength minus five
PercProf: 88.33
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
148.95
34.42
36.53
4.83
165,028.79
147,743.71
1,300.99
1,395.89
11,312.66
Market
0.10
High:
Low:
183.37
114.53
41.36
31.70
312,772.50
17,285.07
2,696.88
(94.89)
12,613.65
(10,011.66)
Portfolio
0.93
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.51
0.32
85,968.44
39.60
70.99
19.89
St. Dev:
High:
0.46
1.97
0.28
0.60
39,057.74
125,026.18
22.04
61.64
5.19
76.18
4.20
24.09
Low:
1.05
0.03
46,910.70
17.56
65.80
15.69
PART 2
110
FIGURE
9.1
Veritas trading using revised RS System No. 1.
the short side. Figure 9.1 shows a sample trade in Veritas, using this version of the
system.
Before we move on, it’s also worth noticing that just because an individual
market has a low relative strength, it doesn’t have to mean it’s in a downtrend (or
vice versa). It still could be in an uptrend, but in the midst of a retracement, which
creates the low relative strength as compared to the market as a whole. Because
many of the short-term systems in this book look for retracements before they
enter on a breakout or other type of short-term chart formation, this system or filter also could work in a contrarian fashion, meaning that we should only look to
enter into stocks with a low relative strength.
TRADESTATION CODE
Variables:
CHAPTER 9
RS System No. 1
111
AllowLong(True), AllowShort(False), StrengthLookback(20), StrengthModifier(-5),
RelStrength(1), AvgRelStrength(1), LongPercRelStrength(1),
ShortPercRelStrength(1), VolStrength(1), AvgVolStrength(1),
LongPercVolStrength(1), ShortPercVolStrength(1),
LongPercStrength(1), ShortPercStrength(1), EntryStrength(1);
If BarNumber = 1 Then
EntryStrength = 1 + StrengthModifier * 0.01;
If Close Data2 <> 0 Then
RelStrength = Close / Close Data2
Else
RelStrength = RelStrength[1];
AvgRelStrength = Average(RelStrength, StrengthLookBack);
If AvgRelStrength <> 0 Then
LongPercRelStrength = RelStrength / AvgRelStrength
Else
LongPercRelStrength = LongPercRelStrength[1];
VolStrength = OBV;
AvgVolStrength = Average(VolStrength, StrengthLookBack);
If AvgVolStrength <> 0 Then
LongPercVolStrength = VolStrength / AvgVolStrength
Else
LongPercVolStrength = LongPercVolStrength[1];
LongPercStrength = LongPercRelStrength * LongPercVolStrength;
If LongPercStrength <> 0 Then
ShortPercStrength = 1 / LongPercStrength
Else
ShortPercStrength = ShortPercStrength[1];
If AllowLong = True and LongPercStrength crosses above EntryStrength Then
Buy ("L-Oct 00") NumCont Contracts Next Bar at Market;
If AllowShort = True and ShortPercStrength crosses above EntryStrength Then
Sell ("S-Oct 00") NumCont Contracts Next Bar at Market;
End;
If EntryPrice > 0 and ShortPercStrength Crosses above EntryStrength Then
ExitLong ("L-Exit") Next Bar at Market;
112
PART 2
If EntryPrice > 0 and LongPercStrength Crosses above EntryStrength Then
ExitShort ("S-Exit") Next Bar at Market;
CHAPTER
10
Meander System V.1.0
Originally presented in January/February 2001, this system is based on the meander indicator, which is a price-band indicator that takes all data points within a bar
into consideration when calculating moving-average and standard-deviation levels. Or, more precisely, it calculates the percentage difference between the previous bar’s closing price (or average price) and the next bar’s different price levels
(open, high, low, and close) before it adds to the latest bar’s closing price (or average price). For a detailed description of this indicator and for programming code,
refer to “Moving beyond the closing price” (Active Trader, October 2000, p. 60)
and www.activetradermag.com/code.htm.
The combination of using all price points and their relative distance from the
previous bar’s close (average price) results in an indicator that hugs price more
closely than other kinds of price bands, making it especially useful for the shortterm trader.
If today’s market action takes us below the lower band (the bands are two
standard deviations away), the system will signal to go long on a limit order, on
the assumption that the market has overextended itself to the short side and in the
short run.
SUGGESTED MARKETS
113
PART 2
114
ORIGINAL RULES
Enter long with a limit order if the market trades below the lower two standard
deviation meander boundary.
Risk 4 percent of available equity per trade.
Exit with a loss if the market drops below the entry price, minus the difference between the forecasted average price and the lower meander boundary.
Exit with a trailing stop (win or loss) if the trade is more than one day old
and the market once again falls below the forecasted lower meander boundary.
Exit with a profit if the market trades above the forecasted upper meander
boundary.
TEST PERIOD
March 1, 1990 to November 11, 2000.
TEST DATA
Daily stock prices for the 30 stocks included in the Dow Jones Industrial Average
(DJIA). A total of $20 per trade has been deducted for slippage and commission.
STARTING EQUITY
$100,000 (nominal).
Because this is a long-only system, it can stall during prolonged market corrections. However, because the system has no trend filter to keep it out of the market
during the early and late stages of a trend, it should react very quickly to favorable
market conditions.
This system clearly illustrates the importance of having a stable profit factor and average profit per trade over a large number of markets and market conditions, rather than a few higher but less robust values. In this case, only 15 out
of 30 markets had a profit factor above 1.10 when analyzed individually; no market was above 1.4. Bottom line: A strategy that incorporates good money management and constantly grinds out even marginal profits can make good money
over time.
The total portfolio profit factor of only 1.2 isn’t eye grabbing. But that’s not
the point. The point is that despite this low profit factor, the system manages to
produce a risk–reward ratio well in line with the closest comparable market index
(DJIA) and a buy-and-hold strategy, while only spending a fraction of the time in
CHAPTER 10
115
the market—24 percent on average per stock, compared to 100 percent per stock
for a buy-and-hold strategy.
Note also that both the worst drawdown and the longest flat time happened
very early on, during the October 1990 scare. Unfortunately, it took a little longer
for the system to recover from this debacle than it did for the market itself.
However, since then, results have been very stable, with very few drawdowns
extending further than 10 percent, and since 1992, no drawdown below 15 percent.
For the original presentation of this system, I wrote that it was just marginally
profitable for no more than 50 percent of the market tested. That was one year ago
(at the time of this writing) and, because this is a long-only system, performance
has continued to deteriorate since then. Table 10.1 shows that of all 65 markets
tested this time, 61 percent were profitable, which resulted in an average profit
factor of 1.05. What is strange with these results is that, despite the low number of
profitable markets and not-so-good performance numbers, the system still produces a relatively high number of profitable trades.
Obviously, it still does a good job identifying good trading opportunities, but
somehow a relatively large number of winners still won’t make up for the losses.
The reason may be that the risk–reward relationship between the forecasted profit target and the expected stop-loss level isn’t what it should be. To explore that, I
started out by moving the profit target one standard deviation further away from
the entry price so that the initial risk–reward relationship, going into the trade,
would be 3:1 instead of only 2:1.
TAB LE
10.1
Average Profitability Using Meander System V.1.0
NetProfit
AvgProfit
PercProf: 61.54
Trades
PercWin
ProfitStD
RiskRatio
Average:
546.52
50.90
24,671.08
48.99
St. Dev:
High:
144.60
691.12
4.19
55.09
125,491.47
150,162.54
221.95
270.94
3,772.27
3,821.25
0.01
Portfolio
Low:
401.93
46.71
(100,820.39)
(172.96)
(3,723.28)
0.22
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Market
Average:
1.05
0.02
99,648.87
66.84
51.12
3.90
St. Dev:
High:
Low:
0.31
1.36
0.74
0.11
0.12
(0.09)
47,720.10
147,368.97
51,928.76
49.37
116.22
17.47
4.62
55.74
46.49
0.55
4.46
3.35
PART 2
116
TAB LE
10.2
Adjusting Risk–Reward Relationship
Long only: Higher target
PercProf: 87.69
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
465.95
122.09
48.22
3.00
95,316.78
96,837.43
239.85
257.05
4,720.86
Market
0.05
High:
Low:
588.04
343.87
51.22
45.23
192,154.21
(1,520.65)
496.90
(17.20)
4,960.71
(4,481.01)
Portfolio
0.93
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.14
0.14
1.28
0.99
0.07
0.07
0.14
(0.00)
83,423.90
42,437.97
125,861.87
40,985.93
45.99
34.13
80.12
11.86
59.26
4.38
63.64
54.88
5.32
0.76
6.08
4.56
Average:
St. Dev:
High:
Low:
As Table 10.2 shows, this made a huge difference in the results. All of a sudden the average profit factor increased to 1.14 and the average profit to $239.85,
making the system quite tradable already. The standard deviations for the average
profit and the profit and risk factors also are very low, which indicates that the
results are very robust.
Concluding that it is better for the trade to run a little longer, the next step was
to get rid of the initial slack period after which the stop was tightened. Table 10.3
shows that this too increased performance a little, but the bad news is that it did so
by sacrificing some robustness and reliability, most clearly indicated by a lower
risk–reward ratio (0.90 compared to 0.93 in Table 10.2). Usually, we would go with
that version of the system that had the highest risk–reward ratio, but because this
time we’re getting rid of a variable completely, it’s worth doing the opposite. The
price we pay for a system that is slightly less curve fitted is a slightly decreased certainty of the outcome. (Not that the system was curve fitted from the beginning.)
Another performance number that could be improved a little is the percentage of time spent in a trade. As you can see, Table 10.3 indicates that it is close to
70 percent, which is a little too much if we would like to trade the system together with several other systems, on a good sized portfolio of markets. However,
because we don’t have that many variables or criteria to work with, we have to add
a new one. In the final decision to keep a new criteria, that criterion needs to
improve results considerably. The criterion I decided to go with was to require that
the day before the entry should be a down day.
Table 10.4 shows the result of this version of the system. And as you can, see
this is a big improvement compared to the version in Table 10.3. The average profit per trade now is $559.05, and the profit factor has now increased to 1.30. But
CHAPTER 10
TAB LE
117
10.3
Removing Slack Period
Long only: Higher target, no slack period
PercProf: 80.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
357.23
92.41
50.52
3.12
108,822.59
117,386.63
354.08
392.64
5,846.09
Market
0.06
High:
Low:
449.64
264.82
53.64
47.40
226,209.22
(8,564.04)
746.72
(38.56)
6,200.17
(5,492.01)
Portfolio
0.90
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.17
0.20
1.38
0.97
0.08
0.09
0.18
(0.01)
89,412.68
43,735.98
133,148.65
45,676.70
46.11
32.16
78.27
13.95
68.12
4.01
72.12
64.11
8.02
1.43
9.45
6.58
Average:
St. Dev:
High:
Low:
the really good stuff is that this improvement also increased the robustness and
reliability of the system. The risk–reward relationship is now at 1.11, which means
that more than 84 percent of all trading sequences now can be expected to produce
a profit. This is further indicated by the lower one standard deviation levels for the
profit and risk factors, which are above one and zero, respectively.
As a final step in this research process, I decided to review the lookback period for the meander calculations, by increasing it to 10 days. Table 10.5 shows that
this too improved the results quite considerably. Again, this is most notable when
TAB LE
10.4
New Criteria Added
Long only: Higher target,
no slack period, one down day
PercProf: 86.15
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
224.11
60.62
53.70
3.74
108,022.77
97,584.38
559.05
504.25
5,541.34
Market
0.09
High:
Low:
284.72
163.49
57.44
49.97
205,607.15
10,438.40
1,063.30
54.80
6,100.39
(4,982.29)
Portfolio
1.11
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.30
0.13
61,157.25
33.37
39.46
7.36
St. Dev:
High:
0.27
1.56
0.12
0.25
31,606.34
92,763.59
23.46
56.83
4.58
44.03
1.17
8.53
Low:
1.03
0.01
29,550.90
9.90
34.88
6.19
PART 2
118
TAB LE
10.5
Increasing lookback Period
Long only: Higher target, no slack period,
one down day, 10-day lookback period
PercProf: 90.77
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
200.98
55.04
52.68
4.23
138,385.04
102,071.61
788.35
652.01
6,378.93
Market
0.12
High:
Low:
256.02
145.95
56.90
48.45
240,456.66
36,313.43
1,440.36
136.33
7,167.28
(5,590.59)
Portfolio
1.21
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.38
0.30
1.68
1.09
0.17
0.13
0.30
0.04
60,164.33
30,118.05
90,282.38
30,046.28
31.99
19.17
51.16
12.83
44.81
4.76
49.57
40.05
9.37
1.70
11.07
7.67
Average:
St. Dev:
High:
Low:
looking at the standard deviation numbers for the profit and risk factors, and the
risk–reward ratio based on the average profit per trade. All these numbers now
indicate that a majority of all trading sequences should produce a profit. And with
the average expected profit per trading sequence at $788.35, this system could
now help us make a good living.
Unfortunately, trading the system from the short side as well did not produce
good enough results to warrant trading from both sides. However, with a little tinkering, tweaking, and experimenting, you should be able to come up with something good. I dare to say that because, even though the short side seems to lower
the overall results quite a bit, the number of profitable trades still is very high,
which means the system is doing a good job identifying good setups for a trade on
the short side as well. It doesn’t work this way probably because the risk–reward
ratio going into the trade needs to be different between the two sides. Alternatively,
the short side should not be traded with limit orders, considering the inherent
upside bias in the stock market. Table 10.6 shows how the latest version of the system behaved when traded from both sides simultaneously.
Figure 10.1 shows what the meander indicator can look like with the lines
adjusted for the long side only. Note in the series of trades that this version of the
system is still quite dangerous in that it can move considerably against the trade as
long as the volatility stays low and it avoids touching the lowest meander line. We
will try to come to grips with this later, when we will try to substitute all current
stops with a set of new ones.
If you compare Tables 10.1 and 10.5 you can see that a disadvantage stemming from all the changes we made is that the average trade length increased by
CHAPTER 10
TAB LE
119
10.6
Trading Both Long and Short Sides
Both sides: Higher target, no slack period,
one day against, 10-day lookback period
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
281.95
76.61
50.64
3.82
60,737.50
131,776.44
227.86
577.92
6,743.58
Market
0.04
High:
Low:
358.57
205.34
54.46
46.82
192,513.94
(71,038.94)
805.78
(350.05)
6,971.45
(6,515.72)
Portfolio
0.39
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.12
0.25
1.37
0.87
0.05
0.12
0.17
(0.07)
104,425.04
65,068.06
169,493.09
39,356.98
69.56
47.83
117.39
21.73
67.78
4.67
72.45
63.10
10.14
1.93
12.08
8.21
Average:
St. Dev:
High:
Low:
FIGURE
PercProf: 69.23
10.1
Long side trading using meander system V.1.0.
PART 2
120
about 200 percent. But because the time spent in a trade remained approximately
the same, while the number of trades decreased by more than 50 percent, we can
conclude that the changes only made the system make the most of the most favorable market situations. In Part 3, we will try to decrease the time spent in a trade
further, to make room for more diversification possibilities.
TRADESTATION CODE
Variables:
AllowLong(True), AllowShort(False), MeanderLookback(10) {Max: 25},
LookbackPoints(0), SetMeanderArray(0), MeanderArrayPos(0), SumDiff(0),
AverageDiff(0), SumSquareError(0), SumError(0), SquareSumError(0),
MeanderStDev(0), Meander(0), MeanderHigh(0), MeanderHighest(0),
MeanderLow(0), MeanderLowest(0);
Array: PriceDiff[100](0);
If BarNumber = 1 Then
LookbackPoints = MeanderLookback * 4;
For SetMeanderArray = 0 To (MeanderLookback - 1) Begin
PriceDiff[SetMeanderArray * 4 + 0] = (Open[SetMeanderArray] Close[SetMeanderArray + 1]) / Close[SetMeanderArray + 1];
PriceDiff[SetMeanderArray * 4 + 1] = (High[SetMeanderArray] Close[SetMeanderArray + 1]) / Close[SetMeanderArray + 1];
PriceDiff[SetMeanderArray * 4 + 2] = (Low[SetMeanderArray] Close[SetMeanderArray + 1]) / Close[SetMeanderArray + 1];
PriceDiff[SetMeanderArray * 4 + 3] = (Close[SetMeanderArray] Close[SetMeanderArray + 1]) / Close[SetMeanderArray + 1];
End;
SumDiff = 0;
For MeanderArrayPos = 0 To (LookbackPoints - 1) Begin
SumDiff = SumDiff + PriceDiff[MeanderArrayPos];
End;
AverageDiff = SumDiff / (LookbackPoints);
SumSquareError = 0;
SumError = 0;
For MeanderArrayPos = 0 To (LookbackPoints - 1) Begin
CHAPTER 10
121
SumSquareError = SumSquareError +
Square(PriceDiff[MeanderArrayPos] - AverageDiff);
SumError = SumError + (PriceDiff[MeanderArrayPos] - AverageDiff);
End;
SquareSumError = Square(SumError);
MeanderStDev = SquareRoot((LookbackPoints * SumSquareError SquareSumError) / (LookbackPoints * (LookbackPoints - 1)));
Meander = Close * (1 + AverageDiff);
MeanderHighest = Close * (1 + AverageDiff + 2 * MeanderStDev);
MeanderHigh = Close * (1 + AverageDiff + MeanderStDev);
MeanderLow = Close * (1 + AverageDiff - MeanderStDev);
MeanderLowest = Close * (1 + AverageDiff - 2 * MeanderStDev);
If AllowLong = True and Close < Close[1] and Close < Open Then
Buy ("L-Jan 01") NumCont Contracts Next Bar at MeanderLow Limit;
If AllowShort = True and Close > Close[1] and Close > Open Then
Sell ("S-Jan 01") NumCont Contracts Next Bar at MeanderHigh Limit;
End;
ExitLong ("L-Stop") Next Bar at MeanderLowest Stop;
ExitLong ("L-Trgt") Next Bar at MeanderHighest Limit;
ExitShort ("S-Stop") Next Bar at MeanderHighest Stop;
ExitShort ("S-Trgt") Next Bar at MeanderLowest Limit;
End;
CHAPTER
11
Relative Strength Bands
Originally presented in March 2001, this system had an error in the original text
in Active Trader magazine. Instead of computing the Bollinger bands for the relative strength line (RSL), as originally stated, the bands should be computed on the
product of all RSV lines (PRSV). The original code did it correctly, but the original system logic explained it all wrong.
This system uses a mix of relative strength (not RSI) analysis and Bollinger
bands to identify markets that are about to break out of congestion areas. In this case,
relative strength is calculated by taking the closing price of market No. 1 and dividing it by market No. 2. Doing this for every bar creates an RSL.
Market No. 1 is stronger than market No. 2 when the RSL is above its n-bar
(in this case 21-day) moving average, and vice versa when the RSL is below its
relative moving average (RMA). Calculating the percentage difference between
the RSL and RMA creates the relative strength value (RSV RSL / RMA). The
higher the value above 1.00, the stronger market No. 1 is in comparison to market No. 2 and vice versa.
To measure the relative strength among several markets, first divide the price
of market No. 1 by the price of each of the other markets, creating several RSLs.
Then calculate a moving average for each RSL. Then calculate the RSV for each
RSL, as described above. Multiply all the RSVs together to create a product RSV
for each market (PRSV). If the end result is above 1.00, market No. 1 is relatively stronger than the majority of the other markets.
Bollinger bands of each PRSV are used to determine whether a particular
market is stronger relative to a large majority of the other markets. If the PRSV for
a specific market is above its one-standard-deviation (SD) Bollinger band, it is rel123
PART 2
124
atively stronger than approximately 84 percent (100 16) of all other markets. (A
one-SD interval should hold approximately 68 percent of all the data, leaving
approximately 16 percent of the data on either side of the SD boundaries. A twoSD interval should hold approximately 95 percent of all the data, leaving approximately 2.5 percent of the data on either side of the SD boundaries.)
Long signals are generated when the PRSV moves above its one-SD boundary; short signals are created when the PRSV moves below its two-SD boundary.
(The asymmetrical SD boundaries are used because of the natural upward drift of
the market and to limit short-side trades for “catastrophe protection.”)
SUGGESTED MARKETS
Index tracking stocks (SPYs, DIAs, QQQs) and stock index futures.
ORIGINAL RULES
Look for long signals only when the PRSV is above its 21-day, one-SD Bollinger band.
Look for short signals only when the PRSV is below its 21-day, two-SD
Bollinger band.
Enter long at the close when the PRSV is above its value of two days ago,
but never on the same bar as a previously exited trade.
Enter short at the close when the PRSV is below its value of two days ago,
but never on the same bar as a previously exited trade.
Risk 2 percent of available equity per trade.
Exit long trades with a trailing stop (profit or loss) if the market drops below the
lowest low of the last two bars, or if the PRSV drops below its value of four days ago.
Exit short trades with a trailing stop (profit or loss) if the market trades above
the highest high of the last two bars, or if the PRSV rises above its value of four
days ago.
Exit all trades on the close if they’re not profitable after eight bars.
TEST PERIOD
March 22, 1990 to December 14, 2000.
TEST DATA
Daily prices for the NASDAQ 100 (NDX), S&P 500 (SPX), and Dow Jones
Industrial Average (DJIA) indices.
STARTING EQUITY
$100,000 (nominal).
CHAPTER 11
125
This test revealed some interesting system characteristics—and there is no way we
could have found out about them using any of the publicly available system testing programs.
Running this system on any of the three individual markets in the portfolio
resulted in less-than-desirable results. The NASDAQ 100 index, for instance, performed fairly well up until the last several months, at which point it gave back all
its previous profits and more.
The DJIA, however, didn’t trade well at all until the last year or so, at which
point it started to post terrific results. The S&P 500 had a steady upward-sloping
equity curve over the test period, but the result was a mere doubling of the initial
equity over more than 10 years of trading. Simply summing the results of the
three markets traded individually would have resulted in the portfolio just breaking even.
But when we combine all markets into one portfolio and use a fixedfractional money management strategy (risking 2 percent of equity per trade), as
we did in this test, things start to happen. The interaction between the markets
creates much better results. First, the steady upward slope of the S&P 500 equity
creates stability. Second, the combined positive returns of the S&P 500 and
NASDAQ over the first several years results in much faster equity growth than that
of any individual markets.
Naturally, the fixed-fractional money management strategy also adds to this
growth in a way other money management techniques do not, because you’re risking more when your equity is increasing and risking less when your equity is
decreasing.
Third, because this system looks at the relative strength among several markets and allows both long and short signals, there are plenty of situations where
one market acts as catastrophe protection for another, which is exactly what happened over the last few months when the NASDAQ underperformed and the DJIA
performed better than ever.
Finally, if two markets signal entry on two consecutive days, it may or may
not be possible to enter into the second market, depending on how much capital is
tied up in the first market. This often prevents entry into bad trades in the weaker
of the markets. Both these factors also work together to produce very low drawdown numbers.
For the original system, I only looked at three indexes: S&P 500, NASDAQ 100,
and DJIA. As it turned out, the result produced by these three markets has not held
up since the system was published. We’ll discuss the reasons for this while we
PART 2
126
make a new attempt to come up with a better, more robust system, given the initial logic.
One major reason for why the results haven’t held up is because the original
system was only tested on three markets, which is far too few to produce results
that can be trusted in the long run. To come to grips with that, I expanded the
research for this book by adding two more indexes to the equation, so that the relative strength of one market was calculated in relation to four other markets,
instead of only two. The code below is set to calculate the relative strength between
the market to be traded and the four markets it’s compared to.
Adding only two more indexes would give us a total of just five trading
sequences, which still isn’t enough. Therefore, I also picked 10 markets each from
the NASDAQ 100 index and the DJIA, respectively, to be compared to eight other
markets each, from their respective indexes. All markets were selected at random.
For example, from the DJIA group, I randomly picked American Express (AXP)
to be compared against Citigroup (C), Eastman Kodak (EK), General Electric
(GE), Home Depot (HD), IBM, United Technologies (UTX), 3M (MMM), and
Merck (MRK). Only AXP would be traded. The other markets are only there to
construct a randomly created RSI for American Express to generate trading signals. In total, this gives us 25 different trading sequences to analyze. Because the
original model was asymmetric in nature, with different rules for long and short
trades, each side will be analyzed individually.
Table 11.1 shows the results of the original model, tested on our 25 different markets. With an average profit of $52.69, a profit factor just above one,
and a risk factor just below zero, the results are not satisfactory, and the conclu-
TAB LE
11.1
Trading Original Relative Strength Bands
PercProf: 48.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
150.24
60.55
36.94
5.36
(5,312.70)
50,710.57
(52.69)
402.95
4,294.81
Market
(0.01)
High:
Low:
210.79
89.69
42.30
31.58
45,397.88
(56,023.27)
350.27
(455.64)
4,242.13
(4,347.50)
Portfolio
(0.13)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.01
(0.00)
55,162.30
42.18
25.43
5.22
St. Dev:
High:
0.29
1.30
0.18
0.18
27,778.81
82,941.11
24.46
66.65
2.57
28.00
0.58
5.80
Low:
0.72
(0.18)
27,383.48
17.72
22.86
4.64
CHAPTER 11
127
sion is that something needs to be done. There are several things we could do,
such as altering the lookback period for the standard-deviation calculations, otherwise making it more or less difficult for the system to generate a signal, or
altering the stop-loss and trailing-stop levels.
Let’s start by making the lookback period for the standard-deviation calculations longer. Table 11.2 shows that using a 200-day lookback period, the average profit is above zero, and the positive result is further confirmed by a profit
factor of 1.08 and a risk factor of 0.02. The results in Table 11.2 are confirmed
by additional tests with other lookback periods, which are not shown. Apparently,
a 21-day lookback period is not enough for this system to produce good results
on the long side.
Going with a longer lookback period than the original 21 days, I arbitrarily
set it to 100 days and continued the research by looking into other parameters
to examine. Table 11.3 shows what happened with the result when I altered the
standard-deviation interval for the entry to zero. With the standard deviation set to
one, as it was originally, the market we’re looking to trade needs to be relatively
stronger than 84 percent of all the markets it’s compared to. With the standard
deviation set to zero, the market we’re looking to trade only needs to be relatively
stronger than 50 percent of all the markets it’s compared against.
Making it easier to enter into the trade by requiring that the market we want
to trade only needs to be relatively stronger than 50 percent of the markets it’s
compared against improved the results considerably. The average profit is now
well above zero at $110.85, and a profit factor above 1.10 indicates the system will
remain profitable when the cost of trading is added as well. The number of prof-
TAB LE
11.2
Altering Lookback Period
Long only: 200-day lookback period
Average:
St. Dev:
High:
Low:
PercProf: 52.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
85.40
51.10
35.27
9.82
13,998.08
46,357.47
6.14
1,109.99
4,338.73
Market
(0.06)
136.50
34.30
45.09
25.45
60,355.55
(32,359.39)
1,116.13
(1,103.84)
4,344.87
(4,332.58)
Portfolio
0.01
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.08
0.02
31,546.25
26.76
15.54
5.71
St. Dev:
High:
0.48
1.55
0.34
0.36
16,273.03
47,819.28
16.35
43.12
6.25
21.78
0.74
6.44
Low:
0.60
(0.33)
15,273.22
10.41
9.29
4.97
PART 2
128
TAB LE
11.3
Setting the Standard Deviations to Zero
Long only: 100-day lookback period, zero st. devs.
PercProf: 64.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
171.04
72.35
36.75
4.50
22,036.35
61,617.06
110.85
397.01
4,633.09
Market
0.02
High:
Low:
243.39
98.69
41.24
32.25
83,653.41
(39,580.71)
507.85
(286.16)
4,743.94
(4,522.24)
Portfolio
0.28
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.11
0.29
0.06
0.18
51,937.08
21,924.01
40.43
24.04
36.46
6.57
6.16
0.74
High:
Low:
1.39
0.82
0.24
(0.12)
73,861.08
30,013.07
64.46
16.39
43.03
29.88
6.90
5.42
itable markets now increased to 64 percent. The number of profitable trades is,
however, still relatively low at 36.75 percent.
Satisfied with these results, I finally decided to test how the system would
fare without the stops applied directly on the market traded. My thinking was that
this would increase the number of profitable trades somewhat, making the system
less nerve-racking to trade. This turned out to be exactly right, but not only that:
As indicated by Table 11.4, all other evaluation parameters soared as well. The
TAB LE
11.4
Revised Relative Strength Bands
Long only: 100-day lookback period,
zero st. devs, no stops
PercProf: 76.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
49.60
26.91
42.16
12.35
115,503.24
188,866.63
3,577.65
6,094.46
20,217.42
Market
0.15
High:
Low:
76.51
22.69
54.50
29.81
304,369.87
(73,363.40)
9,672.11
(2,516.82)
23,795.07
(16,639.78)
Portfolio
0.59
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
2.23
0.72
44,369.24
28.10
54.36
35.21
St. Dev:
High:
1.41
3.64
0.89
1.60
26,314.45
70,683.70
21.07
49.16
9.32
63.68
8.71
43.92
Low:
0.81
(0.17)
18,054.79
7.03
45.04
26.50
CHAPTER 11
129
number of profitable markets continued higher to 76 percent, the average profit
per trade increased to $3,577, the profit factor to 2.23, and according to the risk
factor, we’re now making a whopping 72 cents for every dollar risked.
At first glance, this looks very good indeed, but as already pointed out earlier, when a system produces results this good, they might be too good to be true,
and these results are no exception to that rule. Let’s start by comparing the average profit per trade with the standard deviation for all average profits. Note that
the standard deviation, at $6,094, is almost twice as large as the average profit of
$3,577, which results in a one-standard-deviation interval stretching from
$2,516 to $9,672. Thus, this system still produces a lot of trading sequences with
an average profit per trade below zero, and the chances for the true, always
unknown, average profit to actually be negative are quite high. This annoying fact
is also confirmed by the profit factor that has its lower one-standard-deviation
boundary at 0.81 and the risk factor with its lower one-standard-deviation boundary indicating a loss of 17 cents per dollar risked. Another unwanted feature of this
system is that the average trade length increased from around six days to 35 days,
which no longer can be considered short-term and may be too long when using the
system as a filter for other systems.
The high standard deviations probably ruined the original version of this system. Testing it on only three markets, unknowingly and unwillingly, I managed to
produce a system with a decent hypothetical average profit per trade, but also a
very high standard deviation, thus making it very likely that the system would lose
plenty of money over long periods, which was exactly what happened during the
period following the original testing period.
Granted, the upper one-standard-deviation boundary for the average profit
indicates also a high likelihood that the system will perform better than indicated
by the original research, but good periods are easy to deal with. Of the really bad
periods, we only need one to end our careers as traders (and find a cheaper place
to live). The trick is to keep the likelihood of this happening as small as possible;
for that we also need to sacrifice some upside potential.
Before we move on to the short side, I would like to make one more adjustment, and that is to equalize the lookback periods for the entry and exit formations
that now are set to two and four days, respectively. I would like to do this because
otherwise this system simply has too many adjustable and optimizable variables,
and as we will see later, when we talk about stops and exits, finding robust solutions for more than three variables is very difficult. It also is important that we
keep the entry as simple and logical as possible, with as few rules as possible.
Therefore, if it turns out we’re better off without these variables, or if the results
are inconclusive, the variables will be scratched. If not, they will both be set to the
same value.
As it turned out, the results were rather inconclusive, so both variables will
be scratched. The results of this version of the system can be seen in Table 11.5.
PART 2
130
TAB LE
11.5
More Variables Altered
Long only: 100-day lookback period, zero st. devs,
no stops, no trailing strength test
PercProf: 80.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
57.72
30.85
39.47
13.47
113,784.90
186,768.28
2,746.38
4,494.59
18,421.02
Market
0.13
High:
Low:
88.57
26.87
52.95
26.00
300,553.18
(72,983.38)
7,240.97
(1,748.20)
21,167.40
(15,674.64)
Portfolio
0.61
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
2.19
1.45
3.64
0.74
0.73
0.93
1.65
(0.20)
43,547.04
26,720.15
70,267.19
16,826.89
28.29
20.88
49.17
7.41
54.09
9.54
63.63
44.55
29.72
7.18
36.90
22.54
Average:
St. Dev:
High:
Low:
The two variables we’ve left are RelStrengthLookback and LongStDevs, set to 100
days and zero standard deviations, respectively (see code below).
Despite the rather high likelihood for this version to move into negative territory, this is the version I will take with me to Part 3, where we will try to use it
as a filter for the other more short-term systems featured in this book. To be sure,
at this point the next step could have been to look closer into the results produced
by various combinations of the two remaining optimizable variables. The same
techniques used to find the best and most reliable stops and exit levels, (which we
look at more closely later), also can be used to fine-tune and optimize the entry
variables for robustness and likelihood for future success. I will not do this here,
but you are free to do so if you wish. Note also that if you do, and altering the
LongStDevs variable doesn’t produce significantly improved results while maintaining robustness, it too could be scratched, and you’d be down to one optimizable variable.
Now, let’s follow the same line of reasoning for the short side and see what
we can come up with. Table 11.6 shows the results for the original model, tested
on our 25 different markets. With an average profit of $281.39, a profit factor
below 0.9, and a risk factor of 10 cents, the original results for the short side are
a long way from being satisfactory.
Altering the lookback period, first to 50 days and then to 100 days, indicated that sticking to a shorter lookback period in the neighborhood of 20 to 60 days
is the way to go. In this case, a 50-day lookback period produced a small profit,
whereas the 100-day lookback period dragged the results back into negative territory again. The deteriorating performance from using a too long lookback period
CHAPTER 11
TAB LE
131
11.6
Short Side Trading Using Original Relative Strength Bands
Original system, short only
PercProf: 40.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
56.32
33.20
32.23
10.23
(13,229.68)
29,241.64
(281.39)
1,022.98
4,477.42
Market
(0.11)
High:
Low:
89.52
23.12
42.46
22.01
16,011.96
(42,471.31)
741.59
(1,304.38)
4,196.03
(4,758.81)
Portfolio
(0.28)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
0.88
0.42
1.30
0.46
(0.10)
0.31
0.21
(0.42)
34,525.10
19,478.50
54,003.60
15,046.60
32.43
19.33
51.75
13.10
8.82
2.47
11.29
6.35
5.09
1.05
6.14
4.05
Average:
St. Dev:
High:
Low:
also is confirmed by a test of a 200-day lookback. Therefore, it seems best to stay
with a shorter lookback period for the short side. This also makes sense when
remembering that the original logic for the system said that the short side was only
going to work as catastrophe protection. Using a shorter lookback period, the system will react faster to those swift moves against the general upward drift of the
markets.
With such a short lookback period of 20 to 60 days, to make sure the system
doesn’t trade too often or stop out the more long-term trades on the long side, keep
the standard deviation-based trigger level as far away from the average relative
strength as possible so that only the very weakest markets will be traded. Table
11.7 shows what happened when the standard deviation setting was altered from
two to three standard deviations. Note that the lookback period also is altered to
21 days. Other tests (not shown) with altering lookback periods confirmed that
this was the best combination.
What we would like to happen happens: The profitability of the system
increases considerably using a higher standard deviation setting. Table 11.7 shows
that for a lookback period of 21 days, combined with a three-standard-deviation
trigger level, the average profit per trade has increased to $323.92, the profit factor is now at a decent 1.52, and the risk factor indicates that we could make as
much as 16 cents per dollar risked, on average.
Having decided that we’re better off with a three-standard-deviation entry
level, it’s time to examine the stops applied directly to the market in question.
Table 11.8 shows that a system without stops has a higher average profit per trade
($449.59), but also lower profit and risk factors at 1.30 and 0.08, respectively. The
risk–reward ratio also is slightly lower at 0.17. However, although this version of
PART 2
132
TAB LE
11.7
Altering Standard Deviation (2)
Short only: 21-day lookback period, three st. devs.
PercProf: 44.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
21.32
13.48
38.67
13.19
(2,714.99)
18,602.76
323.92
1,618.80
4,876.61
Market
(0.04)
High:
Low:
34.80
7.84
51.86
25.48
15,887.78
(21,317.75)
1,942.72
(1,294.87)
5,200.54
(4,552.69)
Portfolio
0.20
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.52
1.92
3.44
(0.40)
0.16
0.74
0.89
(0.58)
17,915.29
13,635.08
31,550.37
4,280.21
17.03
13.32
30.35
3.70
3.47
1.65
5.12
1.82
5.21
1.91
7.12
3.30
Average:
St. Dev:
High:
Low:
the system is trading less (approximately 17 trades per market tested), the higher
average profit at $449 produces a higher expected net profit than for the system
with the stops (17 * 449 7633, compared to 21 * 324 6804). (Never mind that
the average net profit is negative in both tables.) Another positive is that this version of the system produces a higher percentage of profitable trades.
If it was up to me, I would go with the system with the highest risk–reward
ratio and lowest standard deviations and trade it on as many markets as possible,
TAB LE
11.8
Removing Stops
Short only: 21-day lookback period,
three st. devs, no stops
PercProf: 44.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
17.24
10.25
41.83
12.82
(4,177.05)
22,461.44
449.59
2,723.90
6,248.83
Market
(0.06)
High:
Low:
27.49
6.99
54.65
29.00
18,284.40
(26,638.49)
3,173.48
(2,274.31)
6,698.41
(5,799.24)
Portfolio
0.17
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.30
0.08
20,753.24
20.12
4.58
8.37
St. Dev:
High:
1.31
2.61
0.66
0.75
14,816.11
35,569.34
14.65
34.77
2.28
6.86
4.27
12.65
(0.00)
(0.58)
5,937.13
5.48
2.30
4.10
Low:
CHAPTER 11
133
but because the results from the two latest versions of the system are somewhat
contradictory, we will do the rest of the testing on both versions (with and without
the stops).
As was the case for the long side, the final step will be to try to equalize the
lookback periods for the entry and exit formations, which now are set to two and
four days, respectively. Testing these variables, both with and without the stops,
continued to produce contradictory results. Keeping the stops produced the best
results with both variables set to two days, but without the stops, the best results
came from scratching both variables completely. When the results are contradictory like this, the rule is that we should strive towards using as few variables as
possible. Therefore, I will scratch both the stops and the trailing-strength test on
the short side as well.
As was the case for the long side, despite the rather high likelihood for this
version of the system to move into negative territory, this is the version I will take
with me to Part 3, where we will try to use it as a trend filter for other systems. To
be sure, at this point the next step could have been to look closer into the results
produced by various combinations of the two variables RelStrengthLookback and
ShortStDevs, which now are set to 21 days and three standard deviations, respectively. The same techniques used to find the best and most reliable stops and exit
levels (which we explore later), also can be used to fine-tune and optimize the
entry variables for robustness and likelihood for future success. I won’t do this
here, but you are free to do so if you wish. Figure 11.1 shows a few long trades in
the Russell 2000 index.
TRADESTATION CODE
This code is for the index version of the system discussed above. For the stocks
version, more stocks (nine) have been used to calculate the total relative strength
for the market to be traded (variable TotRelStrength). To add markets to the calculations, first add the necessary variables (RelStrength.1n, AvgRelStrength.1n,
and PercRelStrength.1n), then add the necessary calculations in accordance with
the logic in the code. For example, the variable AvgRelStrength.1n would be calculated as Average(RelStrength.1n, RelStrengthLookback), the variable
PercRelStrength.1n would be calculated as RelStrength.1n / AvgRelStrength.1n,
and the TotRelStrength variable as PercRelStrength.12 * PercRelStrength.13 * …
* PercRelStrength.1N.
Variables:
AllowLong(True), AllowShort(True), LongRelStrengthLB(100),
ShortRelStrengthLB(21), LongStDevs(0), ShortStDevs(3),
PART 2
134
FIGURE
11.1
Long trading in the Russell 2000 Index.
RelStrength.12(0), LongAvgRelStre.12(0), ShortAvgRelStre.12(0),
LongPercRelStre.12(0), ShortPercRelStre.12(0),
LongTotRelStre(0), ShortTotRelStre(0), LongBaseTriggerCalc(0),
ShortBaseTriggerCalc(0), LongTriggerStrength(0), ShortTriggerStrength(0);
RelStrength.12 = Close / Close Data2;
CHAPTER 11
If AllowLong = True Then Begin
LongAvgRelStre.12 = Average(RelStrength.12, LongRelStrengthLB);
LongPercRelStre.12 = RelStrength.12 / LongAvgRelStre.12;
LongTotRelStre = LongPercRelStre.12 * LongPercRelStre.13 *
LongPercRelStre.14 * LongPercRelStre.15;
LongBaseTriggerCalc = StdDev(LongTotRelStre, LongRelStrengthLB);
LongTriggerStrength = 1 + LongBaseTriggerCalc * LongStDevs;
If MarketPosition = 0 and LongTotRelStre > LongTriggerStrength Then
Buy ("L-Mar 01") NumCont Contracts Next Bar at Market;
End;
If AllowShort = True Then Begin
ShortAvgRelStre.12 = Average(RelStrength.12, ShortRelStrengthLB);
ShortPercRelStre.12 = RelStrength.12 / ShortAvgRelStre.12;
ShortTotRelStre = ShortPercRelStre.12 * ShortPercRelStre.13 *
ShortPercRelStre.14 * ShortPercRelStre.15;
ShortBaseTriggerCalc = StdDev(ShortTotRelStre, ShortRelStrengthLB);
ShortTriggerStrength = 1 - ShortBaseTriggerCalc * ShortStDevs;
If MarketPosition = 0 and TotRelStrength < ShortTriggerStrength Then
Sell ("S-Mar 01") NumCont Contracts Next Bar at Market;
End;
If EntryPrice > 0 and LongTotRelStre < LongTriggerStrength Then
ExitLong ("L-Trail") Next Bar at Market;
If EntryPrice > 0 and TotRelStrength > ShortTriggerStrength Then
ExitShort ("S-Trail") Next Bar at Market;
135
136
PART 2
CHAPTER
12
Rotation
Originally presented in May 2001, this is a longer-term position trading system
designed to trade (from the long side) the two strongest indexes of the Dow Jones
Industrial Average (DJIA), NASDAQ 100, and the S&P 500. As a partial hedge,
the system goes short in the weakest market. The logic behind this system rests on
three assumptions:
The stock market has a long-term upward bias. Always having a long position in two out of three markets should capture this bias.
When a market proves itself to be stronger or weaker than other markets, this
relationship is likely to continue for some time.
If a large, adverse move occurs, it will likely affect all markets simultaneously, but will be particularly devastating for the weakest market; therefore, this
market will be reserved for short trades only.
The indicator used to calculate the relative strength of the three markets is
similar to the 80-day moving average slope (MAS) indicator described in
“Building a Better Trend Indicator” (Active Trader, May 2001, p. 80). However,
instead of analyzing each market directly, the MAS indicator is applied to the ratio
between two markets (i.e., market one divided by market two).
When one market is gaining or losing strength relative to another market, the
80-day MAS indicator’s 20-day slope (today’s MAS—the MAS 20 days ago) will
change direction. Trades are signaled when the short-term volatility is less than the
long-term volatility, as described in the rules.
SUGGESTED MARKETS
Index tracking stocks (SPDRs, DIAs, QQQs), futures, and currencies.
137
PART 2
138
ORIGINAL RULES
Prepare to go long when the MAS indicator signals the trend strength in a market.
(Long positions are established in the two strongest markets.)
Prepare to go short in the market that the MAS indicator identifies as the
weakest of all three markets.
Enter tomorrow (long and short) at the open if the average trading range for
the past three days is less than the average trading range for the last 30 days.
Exit long trades: with a stop loss equal to two times the average trading range
of the three days preceding the entry;
With a trailing stop if the market goes against the trade two times the average trading range of the past three days, deducted from the previous day’s close;
With a profit target if the market moves in the direction of the trade six times
the average trading range of the past three days.
Exit short trades: with a stop loss equal to three times the average trading
range of the day preceding the entry;
With a trailing stop if the market goes against the trade three times the average trading range of the past three days, added to the previous day’s close;
With a profit target if the market moves in the direction of the trade three
times the average trading range of the past three days.
TEST PERIOD
March 1991 to February 2001 (2,500 days of data per market).
TEST DATA
Daily index notations for DJIA, NASDAQ 100, and S&P 500. A total of $20 has
been deducted for slippage and commission per trade.
STARTING EQUITY
$100,000 (nominal).
SYSTEM ANALYSIS
The settings for the MAS indicator in this system are totally unoptimized. It
should be possible to improve the system’s performance by finding a better setting
for this indicator.
The system doesn’t take into consideration the direction of the trend, only
whether one market is stronger or weaker relative to the others. Thus, plenty of situations occur where all three indexes are declining, but the system still trades the
CHAPTER 12
Rotation
139
two strongest of them from the long side. By adding a trend filter to each market,
results should improve considerably.
The asymmetrical stops are designed to distinguish between different market
characteristics that depend on the long-term trend. For example, because markets
generally are more volatile when they fall than when they rally, the trailing stop is
placed further away for the weakest of the markets than it is for the two strongest
ones (to avoid getting stopped out too often).
The trailing stop will only stop out the quickest and most adverse moves
against the trade. If the market moves slowly against the trade for a prolonged period, the trade won’t be exited until the price reaches the stop-loss level.
The reasoning for this system is pretty much the same as for the relative-strength
bands, discussed previously. For the original system, I only looked at the three
indexes: S&P 500, NASDAQ 100, and DJIA. Therefore, I once again had to
expand the research for this book by adding two more indexes and 20 stocks to
achieve statistically reliable results. The code below is set to calculate the relative
strength between one of the indexes and the four indexes it’s compared to.
All stocks were once again picked at random from a population of 30 stocks
in each subgroup. Each stock that was to be traded was compared to eight other
stocks from the same group. For example, from the NASDAQ 100 group, I randomly picked QUALCOMM (QCOM) to be compared against Altera (ALTR),
Bed Bath & Beyond (BBBY), Chiron (CHIR), Dell (Dell), Flextronics (FLEX),
Immunex (IMNX), KLA Tencor (KLAC), and Nextel (NXTL). Only QCOM
would be traded. The other markets are only there to construct a randomly created
relative-strength indication for QCOM to generate trading signals. In total, this
will give us 25 different trading sequences to analyze. Because the original model
was asymmetrical in nature, with different rules for long and short trades, each
side will be analyzed individually.
Table 12.1 shows the results of the original model, traded from the long side
only. As you can see, this is a good start, with very high profit and risk factors. The
major negative is that most standard deviation measures are a little too high.
For the original testing of this system, I decided to always go long, the two
strongest indexes out of the three making up the portfolio. During this research
process, I decided to go long two out of five indexes and long a stock if it belonged
to the four strongest in its group of nine stocks. I settled for these numbers, and
decided to keep them constant, because during the many years of bull market, the
system most likely will seem to perform better the more markets traded, and if
that’s the case, we might just as well trash this relative-strength system completely. However, during this stage of the research process, what seems to be best isn’t
always what will work best in the end. By limiting the number of markets traded
PART 2
140
TAB LE
12.1
Trading Original Rotation System
PercProf: 68.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
47.08
23.77
37.44
9.40
57,123.57
82,533.95
1,197.99
2,684.63
10,348.07
Market
0.11
High:
Low:
70.85
23.31
46.84
28.04
139,657.53
(25,410.38)
3,882.63
(1,486.64)
11,546.07
(9,150.08)
Portfolio
0.45
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.49
0.71
2.20
0.77
0.25
0.40
0.65
(0.15)
44,060.96
20,939.63
65,000.59
23,121.33
31.05
18.61
49.66
12.44
43.96
11.49
55.44
32.47
29.20
13.82
43.02
15.39
Average:
St. Dev:
High:
Low:
at each instance in time, we can risk more and make more on a few well-selected
stocks, than we could trading all stocks at all times. This will become clearer to
you in Part 4, where we discuss various money management issues and how to
always risk the most optimal amount according to your own scientifically determined preferences.
Given that the average trade length is rather high, the most obvious alteration
would be to shorten the lookback periods for the relative strength calculations.
However, doing so would most likely also result in more losing trades, and because
we don’t have that many winners to begin with, I decided to leave the testing of
different lookback periods until last. The first thing then, is to see if we can get rid
of any other variables or criteria. In this case, the most obvious one is the trailing
stop. Doing without it resulted in a slight deterioration of most performance measures (as can be seen in Table 12.2), but because the changes were rather small, it
is still wise to get rid of this criterion to keep the complexity of the system to a
minimum.
Because we started by looking at the stops, the next logical step would be to
look at alternative settings for the stop-loss and profit-target levels. However, as it
turned out, the original settings worked best. Having settled for the exit levels, it
is time to move on to the true range variables, which monitor the volatility of the
market. Altering the lookback period for the long-term true range between 10 and
60 days indicated that the model would work better, the shorter the lookback period. Table 12.3 shows that what we lost in reliability by taking away the trailing
stop, we gained back by making the system more sensitive to the changes in
volatility. The average profit per trade is now at $1,577.59 and the profit factor at
1.46. The risk–reward ratio is its highest so far, at 0.49.
CHAPTER 12
Rotation
141
TAB LE
12.2
Removing Trailing Stop
Long only, no trailing stop
PercProf: 68.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
42.84
21.99
35.34
11.54
55,604.80
82,839.09
1,351.85
3,119.58
11,379.08
Market
0.10
High:
Low:
64.83
20.85
46.88
23.81
138,443.90
(27,234.29)
4,471.43
(1,767.72)
12,730.94
(10,027.23)
Portfolio
0.43
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.43
0.71
2.14
0.73
0.20
0.36
0.56
(0.16)
46,035.35
20,680.92
66,716.27
25,354.43
32.08
18.18
50.25
13.90
45.39
10.91
56.30
34.47
33.62
14.61
48.23
19.01
Average:
St. Dev:
High:
Low:
The original setting for the lookback period for the short-term true range was
three days. If it turns out that the system is getting better, or at least not significantly worse, if we shorten it to one or two days, we should be able to get rid of
this variable as well. As it turned out, however, the best result came from setting
this variable to five days, as Table 12.4 reveals.
With no other variables to change and with the percentage profitable trades
and the average trade length even longer than when we started, it’s finally time to
examine the lookback periods for the relative strength calculations. Altering the
lookback period for the moving average to between 40 and 120 days, and the
TAB LE
12.3
Increasing Sensitivity to Volatility
Long only, no trailing stop, 10-day long true range
PercProf: 76.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
52.56
35.83
36.15
11.03
72,058.83
88,306.76
1,577.59
3,220.31
11,580.11
Market
0.11
High:
Low:
88.39
16.73
47.18
25.12
160,365.60
(16,247.93)
4,797.91
(1,642.72)
13,157.70
(10,002.52)
Portfolio
0.49
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.46
0.63
0.23
0.36
48,207.20
26,902.27
30.16
17.89
53.07
15.53
34.84
18.90
High:
Low:
2.09
0.82
0.59
(0.13)
75,109.47
21,304.93
48.05
12.27
68.60
37.55
53.74
15.94
PART 2
142
TAB LE
12.4
Altering Lookback Period (1)
Long only, no trailing stop, ten-day long true range,
five-day true range
PercProf: 76.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
46.40
30.87
34.72
9.50
68,107.46
83,157.63
1,397.73
2,696.36
12,298.44
Market
0.12
High:
Low:
77.27
15.53
44.22
25.22
151,265.10
(15,050.17)
4,094.10
(1,298.63)
13,696.17
(10,900.70)
Portfolio
0.52
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.45
0.61
2.06
0.85
0.24
0.32
0.57
(0.08)
47,787.58
28,645.41
76,433.00
19,142.17
29.29
16.95
46.24
12.33
53.65
15.37
69.02
38.28
38.82
21.53
60.35
17.29
Average:
St. Dev:
High:
Low:
lookback for the slope of the average between 10 and 60 days, only resulted in
one change, and that was to shorten the lookback period for the slope to 10 days.
Table 12.5 shows that with this change incorporated into the system, the average
profit came out to $1,407, and the profit and risk factors to 1.44 and 0.25, respectively (although we didn’t manage to shorten the trade length).
Although we will take this version of the system with us to the upcoming
parts of the book, it still has several shortcomings that need to be pointed out
TAB LE
12.5
Altering Lookback Period (2)
Long only, no trailing stop, ten-day long true range,
five-day short true range, ten-day slope
PercProf: 76.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
48.12
30.98
34.64
8.33
70,693.68
84,219.20
1,407.35
2,194.06
12,502.29
Market
0.13
High:
Low:
79.10
17.14
42.97
26.31
154,912.88
(13,525.52)
3,601.42
(786.71)
13,909.64
(11,094.94)
Portfolio
0.64
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.44
0.55
0.25
0.29
50,858.30
37,473.66
28.59
16.23
54.74
14.64
38.03
18.25
High:
Low:
1.99
0.89
0.54
(0.04)
88,331.96
13,384.65
44.82
12.36
69.38
40.10
56.28
19.78
CHAPTER 12
Rotation
143
before we move on to the short side. The major shortcoming is that the risk–reward
ratio, at 0.64, isn’t much to brag about. With such a low number, there still is a high
likelihood that the system will lose money over an extended period of time, and
perhaps even over several such periods. Another major negative is the low percentage of profitable trades, which can make the system tough to trade for those
traders who demand a high percentage of winners to feel safe with the system.
Combine this with the low number of trades and the conclusion is that it can take
a long time to get out of one of those losing periods. Finally, the average trade
length is about three times too long for the system to be considered short-term,
according to the definition used in this book. However, in Part 3 the average trade
length still can do us some good, when we try to use this system as a filter for the
other short-term systems.
Moving on to the short side, Table 12.6, which shows the results from the
original system tested on our new markets, indicates this can be a tough cookie to
play with. An average profit of $845 and only 20 percent profitable trading
sequences signal we have a long way to go with this baby.
As with the long side, I started out testing the system without the trailing
stop. Again, a slight loss in performance occurred, but not enough to justify keeping the stop (see Table 12.7). One good thing, compared to the long side, however, is that the short side has a rather high percentage of profitable trades (44.11
percent). When this is the case and the system is still losing money, the best place
to start is with the initial risk–reward relationship when entering the trade. In this
case, both the profit target and the stop loss are placed three average true ranges
away from the entry point.
TAB LE
12.6
Short-side Trading Using Original Rotation System
Trades
PercWin
NetProfit
AvgProfit
PercProf: 20.00
ProfitStD
RiskRatio
Average:
37.84
43.68
(30,953.23)
(845.08)
St. Dev:
High:
31.27
69.11
11.08
54.76
44,520.70
13,567.47
2,556.92
1,711.85
10,769.67
9,924.60
(0.11)
Portfolio
6.57
32.60
(75,473.93)
(3,402.00)
(11,614.75)
(0.33)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
0.86
0.47
(0.12)
0.22
66,079.31
29,751.43
59.15
29.15
25.25
9.73
23.43
12.13
High:
Low:
1.33
0.40
0.10
(0.34)
95,830.74
36,327.89
88.30
30.00
34.99
15.52
35.56
11.30
Low:
Market
PART 2
144
TAB LE
12.7
Removing Trailing Stop for Short-side Trading
Short only, no trailing stop
PercProf: 16.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
37.64
31.11
44.11
11.15
(32,843.74)
46,210.94
(932.72)
2,628.95
10,911.51
Market
(0.12)
High:
Low:
68.75
6.53
55.26
32.96
13,367.20
(79,054.68)
1,696.23
(3,561.68)
9,978.79
(11,844.24)
Portfolio
(0.35)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
0.86
0.47
1.33
0.39
(0.12)
0.22
0.10
(0.35)
66,756.83
31,145.23
97,902.06
35,611.60
59.82
30.73
90.55
29.09
25.48
9.83
35.30
15.65
23.67
12.08
35.74
11.59
Average:
St. Dev:
High:
Low:
Of course, a 1:1 risk–reward relationship can only be profitable if the percentage of profitable trades is at least 50 percent. With a better risk–reward relationship we might, however, get by with considerably fewer winning trades than
that. Basically, we can address this in two ways: We could either place the stop loss
closer to the entry or place the profit target further from the entry. In this case, it
turned out the system did best with a 1 percent stop loss and a 3 percent profit target. The results of this version can be seen in Table 12.8. The average profit is now
TAB LE
12.8
Changing Risk–Reward Relationships
Short only, no trailing stop, 1 percent stop,
3 percent target
PercProf: 28.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
71.36
58.74
25.03
6.42
(20,038.60)
32,195.33
(133.77)
1,117.11
6,578.99
Market
(0.06)
130.10
12.62
31.45
18.61
12,156.73
(52,233.93)
983.35
(1,250.88)
6,445.22
(6,712.75)
Portfolio
(0.12)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
0.91
0.35
(0.09)
0.25
49,783.28
23,790.41
44.82
22.75
19.46
7.75
9.30
2.83
High:
Low:
1.26
0.56
0.16
(0.33)
73,573.68
25,992.87
67.57
22.07
27.21
11.72
12.13
6.47
Average:
St. Dev:
High:
Low:
CHAPTER 12
Rotation
145
up to $133. There is still some way to go, but a considerable improvement,
despite the fact that the tighter stop lowered the percentage profitable trades to just
above 25 percent.
When the time came to alter the long-term and short-term true range calculations, it hit me that down markets more often than not are accompanied by an
increase in volatility, while the original model was looking for the opposite.
Therefore, I decided to reverse the criteria for the volatility, demanding higher
short-term volatility to enter a trade on the short side. This continued to improve
the results (not shown), so for the remainder of the research, this was the logic I
decided to go with.
Experimenting with various true range settings resulted in a long-term true
range of 10 days and a short-term true range of five days, which is the same as
for the long side, but with the logic and ruling reversed. This is good news, as it
indicates some sort of observable way of distinguishing between uptrends and
downtrends. That is, when the five-day volatility is lower than the10-day volatility, the trend is up and vice versa—perhaps something for you to look into on
your own? Table 12.9 shows that the system now is very close to breaking even
and that the number of profitable trading sequences has increased to 36 percent.
We’re getting there.
Experimenting with the lookback periods for the relative strength calculations, the same as for the long side, once again resulted in a 10-day lookback for
the slope, but also in a slightly shorter lookback period for the moving average calculation. In this case, it turned out that a lookback period of 60 days produced the
TAB LE
12.9
Reversed the TR Criteria
3 percent target, 10-day long TR,
five-day short TR, reverse TR criteria
PercProf: 36.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
64.32
49.41
26.55
7.00
(13,380.47)
38,338.45
(19.58)
1,478.71
7,444.69
Market
(0.05)
113.73
14.91
33.54
19.55
24,957.98
(51,718.92)
1,459.13
(1,498.29)
7,425.11
(7,464.27)
Portfolio
(0.01)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
0.96
(0.05)
54,450.76
49.27
21.38
11.07
St. Dev:
High:
0.36
1.32
0.25
0.20
26,916.56
81,367.31
25.83
75.09
7.30
28.68
3.01
14.08
Low:
0.60
(0.30)
27,534.20
23.44
14.08
8.05
Average:
St. Dev:
High:
Low:
PART 2
146
TAB LE
12.10
Short-side Trading Using Revised Rotation System
3 percent target, 10-day long TR,
five-day short TR, reverse TR criteria,
60-day average, 10-day slope
PercProf: 36.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
66.00
46.50
27.24
9.98
(7,415.45)
65,572.19
586.65
2,139.61
7,468.95
Market
(0.02)
112.50
19.50
37.22
17.26
58,156.74
(72,987.65)
2,726.27
(1,552.96)
8,055.60
(6,882.30)
Portfolio
0.27
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.12
0.67
1.79
0.46
0.03
0.42
0.45
(0.39)
55,184.50
30,346.12
85,530.61
24,838.38
48.95
29.72
78.66
19.23
22.32
6.93
29.25
15.39
11.20
3.23
14.42
7.97
Average:
St. Dev:
High:
Low:
Average:
St. Dev:
High:
Low:
best results. Just as was the case with relative strength band system, the short side
needs to operate a little more quickly to be at its best. In all honesty though, I was
surprised that this period wasn’t even shorter. Table 12.10 shows that the short side
also is profitable, with an average profit per trade of $586.65. Never mind that the
risk factor indicates that we’re only likely to make three cents for every dollar
risked.
Looked at all by itself, this seems hardly worth bothering with, but the key
question is when this small profit takes place in relation to the profits and losses
on the long side, and for any other system you’re trading. If it turns out that the
short side essentially broke even until Spring 2000, and only made money over the
last few years, wouldn’t it still be worthwhile to trade the short side during the next
bull market as well, since you never know when the next bear market will start
after that? Figure 12.1 shows a few sample trades for both the long and the short
side on the S&P 500 index during and after the September 11 tragedy. Note how
well the system coped with this situation in this market.
TRADESTATION CODE
Variables:
AllowLong(True), AllowShort(True), LongRelStrenLookb(80),
ShortRelStrenLookb(60), SlopeLookback(10), NoLongMarkets(4),
CHAPTER 12
FIGURE
Rotation
147
12.1
S&P 500 Index trading—September 2001.
NoShortMarkets(2), LongTermTRLookback(10), ShortTermTRLookback(5),
LongStopMulti(2), ShortStopMulti(1), LongTargetMulti(6), ShortTargetMulti(3),
RelStrength.12(1), RelStrength.13(1), RelStrength.14(1), RelStrength.15(1),
LongAvgRelStren.12(1), LongAvgRelStren.13(1),LongAvgRelStren.14(1),
LongAvgRelStren.15(1), ShortAvgRelStren.12(1), ShortAvgRelStren.13(1),
ShortAvgRelStren.14(1), ShortAvgRelStren.15(1), LongAvgSlope.12(0),
LongAvgSlope.13(0), LongAvgSlope.14(0), LongAvgSlope.15(0),
LongTotStrength.1(0), ShortAvgSlope.12(0), ShortAvgSlope.13(0),
ShortAvgSlope.14(0), ShortAvgSlope.15(0), ShortTotStrength.1(0),
RelStrength.21(1), RelStrength.23(1), RelStrength.24(1), RelStrength.25(1),
LongAvgRelStren.21(1), LongAvgRelStren.23(1),LongAvgRelStren.24(1),
LongAvgRelStren.25(1), ShortAvgRelStren.21(1),
ShortAvgRelStren.23(1),ShortAvgRelStren.24(1), ShortAvgRelStren.25(1),
148
PART 2
LongAvgSlope.21(0), LongAvgSlope.23(0), LongAvgSlope.24(0),
LongAvgSlope.25(0), LongTotStrength.2(0), ShortAvgSlope.21(0),
ShortAvgSlope.23(0), ShortAvgSlope.24(0), ShortAvgSlope.25(0),
ShortTotStrength.2(0), RelStrength.31(1), RelStrength.32(1), RelStrength.34(1),
RelStrength.35(1), LongAvgRelStren.31(1), LongAvgRelStren.32(1),
LongAvgRelStren.34(1), LongAvgRelStren.35(1),
ShortAvgRelStren.31(1), ShortAvgRelStren.32(1), ShortAvgRelStren.34(1),
ShortAvgRelStren.35(1), LongAvgSlope.31(0), LongAvgSlope.32(0),
LongAvgSlope.34(0), LongAvgSlope.35(0), LongTotStrength.3(0),
ShortAvgSlope.35(0), ShortTotStrength.3(0), RelStrength.41(1), RelStrength.42(1),
RelStrength.43(1), RelStrength.45(1), LongAvgRelStren.41(1),
LongAvgRelStren.42(1), LongAvgRelStren.43(1), LongAvgRelStren.45(1),
ShortAvgRelStren.41(1), ShortAvgRelStren.42(1), ShortAvgRelStren.43(1),
ShortAvgSlope.45(0), ShortTotStrength.4(0), RelStrength.51(1), RelStrength.52(1),
RelStrength.53(1), RelStrength.54(1), LongAvgRelStren.51(1),
LongAvgRelStren.52(1),LongAvgRelStren.53(1), LongAvgRelStren.54(1),
ShortAvgRelStren.51(1), ShortAvgRelStren.52(1),ShortAvgRelStren.53(1),
ShortAvgSlope.54(0), ShortTotStrength.5(0), MinLongStrength(0),
MaxShortStrength(0), LongTermTrueRange(0), ShortTermTrueRange(0);
LongAvgRelStren.12 = Average(RelStrength.12, LongRelStrenLookb);
LongAvgSlope.12 = LongAvgRelStren.12 / LongAvgRelStren.12[SlopeLookback];
CHAPTER 12
Rotation
149
ShortAvgRelStren.12 = Average(RelStrength.12, ShortRelStrenLookb);
ShortAvgSlope.12 = ShortAvgRelStren.12 / ShortAvgRelStren.12[SlopeLookback];
LongTotStrength.1 = LongAvgSlope.12 * LongAvgSlope.13 * LongAvgSlope.14 *
LongAvgSlope.15;
ShortTotStrength.1 = ShortAvgSlope.12 * ShortAvgSlope.13 * ShortAvgSlope.14
* ShortAvgSlope.15;
RelStrength.21 = Close Data2 / Close;
RelStrength.23 = Close Data2/ Close Data3;
LongAvgSlope.25;
* ShortAvgSlope.25;
PART 2
150
LongAvgSlope.35;
* ShortAvgSlope.35;
CHAPTER 12
Rotation
151
LongAvgSlope.45;
* ShortAvgSlope.45;
LongAvgSlope.54;
* ShortAvgSlope.54;
MinLongStrength = NthMaxList(NoLongMarkets, LongTotStrength.1,
LongTotStrength.2, LongTotStrength.3, LongTotStrength.4, LongTotStrength.5);
MaxShortStrength = NthMinList(NoShortMarkets, ShortTotStrength.1,
152
PART 2
ShortTotStrength.2, ShortTotStrength.3, ShortTotStrength.4, ShortTotStrength.5);
LongTermTrueRange = AvgTrueRange(LongTermTRLookback);
ShortTermTrueRange = AvgTrueRange(ShortTermTRLookback);
If AllowLong = True and LongTotStrength.1 >= MinLongStrength and
LongTermTrueRange > ShortTermTrueRange Then
Buy ("L-May 01") NumCont Contracts Next Bar at Market;
If AllowShort = True and ShortTotStrength.1 <= MaxShortStrength and
LongTermTrueRange < ShortTermTrueRange Then
Sell ("S-May 01") NumCont Contracts Next Bar at Market;
End;
ExitLong ("L-Stop") Next Bar at EntryPrice –
(ShortTermTrueRange * LongStopMulti) Stop;
ExitLong ("L-Trgt") Next Bar at EntryPrice +
(ShortTermTrueRange * LongTargetMulti) Limit;
ExitShort ("S-Stop") Next Bar at EntryPrice +
(ShortTermTrueRange * ShortStopMulti) Stop;
ExitShort ("S-Trgt") Next Bar at EntryPrice –
(ShortTermTrueRange * ShortTargetMulti) Limit;
End;
CHAPTER
13
Volume-weighted Average
Originally presented in July 2001, this system tries to identify short-term corrections that have exhausted themselves by ending with a final move in the direction
of the correction accompanied by an increase in volume. When this happens, the
system enters in the opposite direction if the market turns and takes out the highest high or lowest low for the previous two days. The direction of the correction is
indicated by the latest closing price in relation to a short-term volume-weighted
average (VWA), which is similar to a regular exponential moving average.
Calculating the VWA is a two-step process:
Calculate the current average volume (AV) in relation to the highest average
volume (HAV) and lowest average volume (LAV) of the lookback period. For
example, if the lookback period is set to nine days, as it is for this particular system, calculate AV for the last nine days together with HAV and LAV for the same
nine days. Then, take the difference between AV and LAV and divide it by the difference between HAV and LAV. The result will be a value between zero and one.
If this relative value (RV) is increasing from one bar to the next, the average volume is not only increasing, it is also moving closer to a short-term extreme level.
Reverse the reasoning if RV is decreasing. The formula for calculating RV looks
like this:
RV (AV LAV) / (HAV LAV)
Multiply the closing price (C) for each bar by RV, and multiply the previous
bar’s VMA (PVMA) by one minus RV. Then add the two totals together to reach
the VWA for the current bar. The VWA for the first bar in the sequence will be its
closing price multiplied by RV. The higher the average volume, the higher the RV,
153
PART 2
154
and the more weight given to the latest closing price. A simplified formula for calculating VWA looks something like this:
VWA RV * C (1 RV) * PVWA
SUGGESTED MARKETS
Stocks and index shares (SPDRs, DIAs, QQQs).
ORIGINAL RULES
Prepare to go long if today’s closing price is below VWA and if VWA is lower
today than yesterday.
Prepare to go short if today’s closing price is above VWA and if VWA is
greater today than yesterday.
Enter long tomorrow if the market trades above the highest high of the previous two days. Risk 1 percent of available equity per trade.
Enter short tomorrow if the market trades below the lowest low of the previous two days. Risk 1 percent of available equity per trade.
Exit all trades: On the close, if the market does not follow through on its
move that triggered the trade, by also closing above (below for short trades) the
VWA;
If the market moves against you more than 4 percent.
TEST PERIOD
September 1991 to April 2001 (2,500 days of data per market).
TEST DATA
Daily notations for the 30 stocks making up the Dow Jones Industrial Average
(DJIA). A total of $20 per trade was deducted for slippage and commission.
STARTING EQUITY
$100,000 (nominal).
For this particular system, we took the liberty of defining the trend using hindsight, allowing only long trades until April 1990 and only short trades thereafter
(basically just to provide an example of how this can be done). While this type of
CHAPTER 13
155
hindsight analysis is not the way to go during the final stages of your system
design and testing process, it is a valid approach in the initial stages, when you
want to know how the system would have operated in “the best of both worlds.”
This will give you an indication if the idea is worth pursuing any further.
Other than that, this system provides no other type of technical indicator to
measure the direction or strength of the longer-term trend. Therefore, it should be
possible to still achieve good results by substituting for the hindsight trend indicator a good trend filter, such as a long-term moving average.
The nine-day lookback period for the VWA is totally unoptimized.
Experimenting with this number should make it possible to increase performance.
It also is possible to reverse the reasoning for the second equation in the composition of VWA and give the latest closing price less weight, the higher the volume.
The new formula would look like this: VWA (1 RV) * C RV * PVWA. In
this way, the distance between the VWA and the closing price widens during highvolume breakouts, which gives the market more wiggle room when trending.
From Tables 13.1 and 13.2, it seems that this system has held up well since it was
put together, and that it’s also doing exceptionally well on previously untested markets. Granted, the system is losing money on the short side, but that doesn’t have
to be a bad thing as long as the profits on the short side come when the long side
is doing bad.
For the original article in Active Trader magazine, this system was fitted with
a trend filter that operated with the benefit of hindsight. As mentioned, this is a
TAB LE
13.1
Retesting Original Volume-weighted Average System
Average:
St. Dev:
High:
Low:
PercProf: 87.30
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
78.94
27.48
44.73
7.82
52,768.38
46,759.75
758.85
870.70
4,889.35
Market
0.14
106.41
51.46
52.55
36.91
99,528.13
6,008.64
1,629.56
(111.85)
5,648.20
(4,130.50)
Portfolio
0.87
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.70
0.34
25,968.61
20.06
10.13
5.42
St. Dev:
High:
0.77
2.46
0.33
0.67
14,556.43
40,525.04
12.64
32.69
2.74
12.87
0.65
6.07
Low:
0.93
0.01
11,412.18
7.42
7.39
4.77
PART 2
156
TAB LE
13.2
Less Tantalizing Results for the Short Side
PercProf: 39.68
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
19.40
4.24
36.87
13.04
(2,394.46)
26,927.83
(28.61)
1,654.87
4,875.63
Market
(0.08)
High:
Low:
23.64
15.15
49.91
23.83
24,533.37
(29,322.29)
1,626.26
(1,683.47)
4,847.02
(4,904.24)
Portfolio
(0.02)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.21
1.49
2.70
(0.28)
0.00
0.54
0.54
(0.54)
21,910.62
14,267.27
36,177.89
7,643.35
20.05
13.32
33.36
6.73
1.93
0.99
2.92
0.94
3.90
1.10
5.00
2.80
Average:
St. Dev:
High:
Low:
valid approach when you want to see how the system would have performed given
ideal conditions that could only be observed with the help of hindsight. It is not,
however, recommended that you trade a system with such a filter built into it. The
first thing to do in this round of renewed research is to get rid of the trend filter.
Originally, the system was also fitted with a 4 percent stop loss. As it turned
out, this stop loss made absolutely no difference whatsoever. It was only there for
money management purposes, but because we will address the money management issue later, we can get rid of the stop loss for now and save ourselves an optimizable variable. Table 13.3 shows that the system continues to perform well on
the long side without the stop loss and the trend filter. The average profit did
decrease by close to $200, but the risk–return ratio is still at a healthy 0.86 and,
because of a few more trades, the average net profit still came out to close to
$50,000. Unfortunately, however, the short side (Table 13.4) did not do as well as
the long side, primarily because of an increasing number of bad trades during the
long bull market in the 1990s. A profit factor of 0.92 and an average profit per
trade of $119 indicates that we are losing money at a slow but steady rate.
Just to make sure that the logic behind the system was correct, I decided to
test the entry rules. Instead of demanding the close to be lower than the volumeweighted average for a long trend, I wanted it to be higher than the average, more
in line with a normal technical-analysis trend interpretation (reverse the reasoning
for the short side). But this did not better the results for either side. The same was
true for altering the way to calculate the average, as suggested at the end of the
original system presentation, by giving the latest closing price less weight the
higher the volume for the moving-average calculation. (No use in showing the
results for either one of these alterations.)
CHAPTER 13
TAB LE
157
13.3
Removing Stop Loss and Trend Filter, Long-side Trades
Long only: No trend filter, no stop loss
PercProf: 84.13
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
98.24
28.02
43.57
6.76
49,535.85
55,195.62
560.13
651.52
4,984.54
Market
0.10
126.26
70.21
50.34
36.81
104,731.47
(5,659.77)
1,211.65
(91.39)
5,544.67
(4,424.41)
Portfolio
0.86
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.45
0.51
1.97
0.94
0.23
0.25
0.47
(0.02)
37,398.52
21,925.40
59,323.92
15,473.12
25.83
15.65
41.48
10.18
12.58
2.55
15.13
10.02
5.31
0.57
5.88
4.73
Average:
St. Dev:
High:
Low:
Average:
St. Dev:
High:
Low:
Keeping the original rules and calculations, let’s look at another strange feature of this system: Namely, the condition for staying in a trade, which doesn’t
have to be fulfilled at the entry. Because the close needs to be above (below for a
short trade) the volume-weighted average to stay in the trade, it also would make
sense to ask the price to cross the volume-weighted average instead of the highest
high of the last two days (lowest low for a short trade) to trigger a trade. As it turns
out, however, this actually lowers the results somewhat—probably because the sys-
TAB LE
13.4
Short-side Trades without Stop Loss and Trend Filter
Short only: No trend filter, no stop loss
PercProf: 34.92
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
96.75
31.42
33.24
6.51
(19,619.26)
48,768.85
(119.43)
687.87
4,098.89
Market
(0.06)
128.17
65.33
39.75
26.73
29,149.59
(68,388.10)
568.44
(807.31)
3,979.45
(4,218.32)
Portfolio
(0.17)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
0.92
(0.07)
53,285.06
47.99
9.16
3.97
St. Dev:
High:
0.41
1.33
0.24
0.17
28,905.17
82,190.23
28.57
76.56
2.12
11.29
0.57
4.53
Low:
0.52
(0.32)
24,379.89
19.42
7.04
3.40
Average:
St. Dev:
High:
Low:
PART 2
158
tem does a good job in catching the anticipated move early with its original rules,
instead of waiting for the move to get started.
Having tested the logic behind the system (which was obviously there for
some reason I had forgotten about), it is time to test the lookback periods for the
volume-weighted average and its highest high and lowest low values. As it turned
out, there was no rhyme or reason to how the results changed with individual
changes in the lookback periods. Therefore, I set both lookback periods to the
same value and thereby got rid of another optimizable variable before I tested for
lookback periods longer and shorter than the original nine days.
The testing indicated that the long side worked best, with a slightly longer
lookback period of 21 days, which also equals one month. Good results for surrounding lookback periods, such as 18 to 25 days confirmed that this also is a
robust solution. For the short side, the best and most robust results came with a
lookback period of 10 days, or two weeks. By the way, I like it when the lookback
periods align themselves with calendar periods: It helps me make sense of and put
trust in the logic behind the system, even though I shouldn’t have a problem with
that, since I built it myself in the first place.
Table 13.5 shows that the average profit for the long side now is $661, with
a risk–reward ratio of 0.95. These very good numbers indicate that the system has
a large likelihood to be profitable in the future as well as in the past. This is further confirmed by the lower standard deviation boundaries for the profit and risk
factors, which both are safely above one and zero, respectively. The risk factor tells
us that we can expect to make 26 cents for every dollar risked, which is very good
indeed.
TAB LE
13.5
Altering Lookback Period for Long-side Trading
Long only: No trend filter, no stop loss,
21-day lookback
PercProf: 87.30
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
110.92
30.86
42.80
6.58
64,023.40
56,981.64
661.56
695.88
5,423.76
Market
0.11
High:
Low:
141.78
80.06
49.39
36.22
121,005.04
7,041.77
1,357.45
(34.32)
6,085.32
(4,762.20)
Portfolio
0.95
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.49
0.47
0.26
0.23
37,481.14
18,477.53
24.85
14.51
15.08
3.00
5.64
0.75
High:
Low:
1.96
1.02
0.49
0.03
55,958.67
19,003.61
39.36
10.34
18.08
12.07
6.40
4.89
CHAPTER 13
TAB LE
159
13.6
Altering Lookback Period for Short-side Trading
Short only: No trend filter, no stop loss,
10-day lookback
PercProf: 33.33
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
99.98
31.31
32.95
7.14
(22,515.10)
48,348.58
(126.88)
871.36
4,023.59
Market
(0.06)
131.29
68.68
40.08
25.81
25,833.48
(70,863.68)
744.48
(998.24)
3,896.71
(4,150.47)
Portfolio
(0.15)
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
0.97
0.74
1.71
0.23
(0.06)
0.30
0.24
(0.36)
53,793.11
31,310.98
85,104.09
22,482.12
48.74
30.96
79.71
17.78
9.37
2.16
11.53
7.20
3.92
0.53
4.45
3.39
Average:
St. Dev:
High:
Low:
Average:
St. Dev:
High:
Low:
The short side is still not as good as it was in the original model, using a trend
filter based on hindsight. But, as Table 13.6 indicates, a profit factor of 0.97 and
a risk factor of 0.06 (meaning we’re losing six cents for every dollar risked) still
isn’t too bad, considering the long up trend this side of the system had to battle.
These versions of the system will go with us to the next section, where we will try
to improve on the results further by adding a few stops and exits. Hopefully this
will make the short side profitable as well. Figure 13.1 shows one good short trade
in Merck, followed by a series of whipsaw trades, some winners, and some losers.
TRADESTATION CODE
Variables:
AllowLong(True), AllowShort(True), AverageUpLength(21),
AverageDownLength(10), TriggerLength(2),
AverageUpVolume(0), HighAvgUpVolume(0), LowAvgUpVolume(0),
RelAvgUpVolume(0), InvRelAvgUpVolume(0), AvgVolumeUpWeight(0),
VolWeightedUpAvg(0), AverageDownVolume(0), HighAvgDownVolume(0),
LowAvgDownVolume(0), RelAvgDownVolume(0), InvRelAvgDownVolume(0),
AvgVolumeDownWeight(0), VolWeightedDownAvg(0);
If AllowLong = True Then Begin
PART 2
160
FIGURE
13.1
Merck trading using revised volume-weighted average system.
AverageUpVolume = Average(Volume, AverageUpLength);
HighAvgUpVolume = Highest(AverageUpVolume, AverageUpLength);
LowAvgUpVolume = Lowest(AverageUpVolume, AverageUpLength);
RelAvgUpVolume = (AverageUpVolume - LowAvgUpVolume) /
(HighAvgUpVolume - LowAvgUpVolume);
InvRelAvgUpVolume = 1 - RelAvgUpVolume;
VolWeightedUpAvg = RelAvgUpVolume * AvgPrice +
InvRelAvgUpVolume * VolWeightedUpAvg;
If MarketPosition = 0 and Close < VolWeightedUpAvg and
VolWeightedUpAvg < VolWeightedUpAvg[1] Then
Buy ("L-July01") Next Bar NumCont Contracts at Highest(High,
TriggerLength) Stop;
End;
If AllowShort = True Then Begin
CHAPTER 13
161
AverageDownVolume = Average(Volume, AverageDownLength);
HighAvgDownVolume = Highest(AverageDownVolume, AverageDownLength);
LowAvgDownVolume = Lowest(AverageDownVolume, AverageDownLength);
RelAvgDownVolume = (AverageDownVolume - LowAvgDownVolume) /
(HighAvgDownVolume - LowAvgDownVolume);
InvRelAvgDownVolume = 1 - RelAvgDownVolume;
VolWeightedDownAvg = RelAvgDownVolume * AvgPrice +
InvRelAvgDownVolume * VolWeightedDownAvg;
If MarketPosition = 0 and Close > VolWeightedDownAvg and
VolWeightedDownAvg > VolWeightedDownAvg[1] Then
Sell ("S-July01") Next Bar NumCont Contracts at Lowest(Low,
TriggerLength) Stop;
End;
If MarketPosition = 1 and Close < VolWeightedUpAvg Then
ExitLong on Close;
If MarketPosition = -1 and Close > VolWeightedDownAvg Then
ExitShort on Close;
CHAPTER
14
Harris 3L-R Pattern Variation
Originally presented in November 2001, this system shows that you don’t have
to be a rocket scientist to come up with a profitable trading strategy. It is based on
a simple pattern developed by Michael Harris (www.TradingPatterns.com) and
previously featured in Active Trader (“Keeping It Simple,” September 2001, p.
82). It consists of two simple principles that are likely to remain true, no matter
how much the general market conditions change.
The first principle is that no market is likely to continue in the same direction more than a few days in a row before it reverses. That doesn’t necessarily
mean the longer-term trend has to change or that the move in the opposite direction will be large enough to produce a profitable trade. For example, if the market
were truly random (they almost are, but not quite), the likelihood for three up or
down days in a row would be a mere 12.5 percent (0.5 * 0.5 * 0.5 0.125).
The second principle states that you are better off trading with the momentum of the market and, more often than not, using breakout trades. In this case, the
breakout is signaled on a higher high than the high of three days ago.
When both of the prerequisites have been met, enter a long position on the
next open and stay in the trade for either a 12 percent profit or a 4 percent loss.
This system is changed slightly from the one featured in the September 2001 issue,
because the profit–loss ratio is changed from 1:1 to 3:1 (throughout the rest of the
book, I use the term risk–reward relationship to describe this).
163
PART 2
164
SUGGESTED MARKETS
Stocks, stock index futures, index shares (SPYs, DIAs, QQQs), commodity
futures, and currencies.
ORIGINAL RULES (LONG TRADES ONLY)
Go long on the next open if today’s high is higher than the high three days ago,
yesterday’s low is lower than the low two days ago, and the low two days ago is
lower than the low three days ago.
Risk 1 percent of available equity per trade for all trades.
Exit all trades with a loss if the market moves against the position by 4 percent or more.
Exit all trades with a profit if the market moves in favor of the position by 12
percent or more.
TEST PERIOD
January 1992 to August 2001 (2,500 days of data per security).
TEST DATA
Daily stock prices for the 30 highest capitalized stocks in the NASDAQ 100,
excluding Intel and Microsoft (which also are in the Dow Jones Industrial Index).
A sum of $20 per trade has been deducted for slippage and commission.
STARTING EQUITY
$100,000 (nominal).
This version of the system does not take into account the opening price before the
trade is entered. One way to filter out a few likely losers is to enter a trade only on
those days the open confirms the previous day’s breakout, by either opening higher than the previous day’s close or at least not so low that the breakout is completely negated. Along the same lines, it also could be a good idea to make sure
the market doesn’t open too high above the breakout, lest the better part of the
move is over before you get a chance to enter.
The original 1:1 profit–loss relationship did not work very well. I therefore
arbitrarily changed it to a 4 percent stop loss and a 12 percent profit target. Both
stops are, however, completely unoptimized, which means a little fine-tuning
CHAPTER 14
165
could help. It also could be a good idea to add a trailing stop that, for example,
never lets you lose more than half your profits, or that tightens as your profits
increase. To avoid tying up valuable resources in trades that go nowhere, a timebased stop could be added that exits all trades after a certain number of days, no
matter what.
As usual, it also would be a good idea to add a trend filter, such as a longterm moving average, and allow the system to trade short by reversing the logic. It
has been proven that a trend filter—allowing only those trades that go with the
direction of the underlying trend—improves performance in most systems.
Finally, note that many of the stocks traded in this example weren’t tradable
until a few years ago, which explains the exceptionally long flat period halfway
through the testing period (not shown). Had we been able to test the same 30
stocks throughout the entire period, it’s highly likely that it would have increased
performance considerably. This is indicated by the latest drawdown, which comes
nowhere near the current drawdown in the NASDAQ, and which would probably
have been smaller still had we traded the market from the short side as well.
Testing this system anew over the period January 1990 to February 2002, on the
30 stocks making up Dow Jones index, the 30 stocks with the highest market
capitalization in NASDAQ 100, and five different stock indexes (Dow
Industrial, S&P 500, NASDAQ 100, S&P MidCap, and Russell 2000) show that
the results on the long side hold up well. An average profit factor of 1.48 and an
average risk factor of 0.28 are not bad. A risk–reward ratio of 0.96 means that
we can be pretty sure that the average profit will not turn negative when the system is traded for real. Also, of all the markets tested, more than 80 percent were
profitable, which is very good indeed. Table 14.1 shows the combined results
from all markets tested.
As Table 14.2 shows, adding the short side to the equation seems not to have
been such a good idea. The number of profitable markets sank to 61.5 percent, the
profit factor is just barely high enough to compensate for slippage and commission, and the risk factor is a mere 6 cents per dollar risked. The risk–reward ratio
for the entire portfolio, which measures the risk-adjusted return by dividing the
average profit per trade by the standard deviation of the average profit per trade,
also is too low, at 0.04, thus indicating that the trades produced by this system are
all over the place.
One big negative with this system is its average trade lengths of 23 and 12
days, respectively. This is way too long, considering that the trade is based on a
three-day pattern and the fact that it should be a short-term strategy. Looking
through the charts, it is easy to find trades that last for as long as six months and
longer. We will talk more about this in Part 3, where we discuss various types of
PART 2
166
TAB LE
14.1
Retesting Results of Harris 3L-R Pattern System
PercProf: 81.54
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
50.20
11.73
34.10
7.70
62,126.82
64,447.90
1,295.04
1,344.95
8,337.05
Market
0.15
High:
Low:
61.93
38.47
41.80
26.40
126,574.73
(2,321.08)
2,639.99
(49.90)
9,632.09
(7,042.01)
Portfolio
0.96
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.48
0.52
2.00
0.96
0.28
0.29
0.57
(0.01)
42,058.76
18,687.90
60,746.66
23,370.87
31.15
18.84
49.99
12.31
25.77
14.41
40.18
11.37
23.55
19.33
42.88
4.22
Average:
St. Dev:
High:
Low:
stops and exit techniques. For now, let’s just state that we should not stay in a trade
for any longer than what can be validated by the entry signal and the underlying
fundamental reason why this signal came about. Obviously, it does not make sense
to enter into a six-month trade based on a three-day pattern.
The reason why this currently is the case can be found in the rudimentary
stop-loss and profit-target exits. The stop was set in such a way that it would be
sufficiently far from the entry so that we wouldn’t be stopped out immediately
TAB LE
14.2
Short-side Trading
Original system, both sides
PercProf: 61.54
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
105.51
20.61
26.71
5.53
21,948.35
75,765.43
30.20
822.11
6,720.68
Market
(0.02)
High:
Low:
126.11
84.90
32.24
21.18
97,713.78
(53,817.09)
852.31
(791.91)
6,750.87
(6,690.48)
Portfolio
0.04
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.10
0.06
76,602.44
63.90
32.56
12.80
St. Dev:
High:
0.29
1.39
0.20
0.26
31,358.80
107,961.24
31.53
95.43
13.19
45.75
5.49
18.29
Low:
0.81
(0.14)
45,243.64
32.38
19.37
7.30
CHAPTER 14
167
after the entry in case of a high-volatility day, which hasn’t been all that uncommon recently. To achieve a desired 3:1 risk–reward relationship, the profit target
then needed to be as far as 12 percent away from the entry, which, as indicated by
the trade length, is too far for a short-term system.
To see if we can make the system a little more short-term, let’s see how it will
function with a stop loss of 1 percent together with a profit target of 3 percent (for a
3:1 risk–reward relationship). Table 14.3 shows that the average profit per trade for
all long trades diminished considerably compared to the original system, as did the
risk–reward ratio for all markets, as indicated by a risk ratio of 0.58. The profit and
risk factors also decreased a great deal, but at least the profit factor is within a tolerable limit at this stage of the research. One worrying thing is that the number of
trades didn’t increase that much at all, despite a shortening of the average trade
length. Apparently, this is a very rare pattern, and perhaps it should be treated as
such, letting it continue to catch those longer-term moves on the long side. Let’s stick
to the short-term strategy for now, however, and see if we can improve it further.
My main criticism when I tested this system for Active Trader was that no
criteria existed for the opening price on the day for the entry. Entering blindly on
the open might result in an entry so far away from the break through the trigger
level that the reason for the trade might have not only been negated, but also even
reversed. Making the system more short term makes it even more important to do
something about this.
To check if the results could be improved by adding some sort of volatility
criteria for the open, I altered the entry rule to require an opening price not more
than one average true range (measured over the last 20 days) from the trigger level,
TAB LE
14.3
Changed Risk–reward Relationship
Long only, 3:1 risk–reward relationship
PercProf: 73.85
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
64.55
15.70
37.41
7.17
15,271.85
24,347.84
267.46
459.34
3,483.27
Market
0.06
High:
Low:
80.25
48.85
44.58
30.24
39,619.68
(9,075.99)
726.80
(191.88)
3,750.73
(3,215.81)
Portfolio
0.58
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.21
0.11
23,308.50
20.15
6.33
4.01
St. Dev:
High:
0.31
1.51
0.18
0.29
10,809.47
34,117.97
9.93
30.08
2.84
9.17
1.65
5.66
Low:
0.90
(0.07)
12,499.03
10.22
3.50
2.36
PART 2
168
which is the high from four days prior. The test was done on the system with the
1 percent stop and the 3 percent profit target. But because this did little to better
the results, I decided to stay with the original logic.
However, because it didn’t seem to matter where the opening and the entry
price were in relation to the trigger level, which was the high four days before the
open, it is questionable if the opening price is needed at all. What if we just enter
one day earlier with a stop order, immediately when the trigger level is hit? Tables
14.4 and 14.5 show the result from this test for the short-term risk–reward relationship version of the system.
And what do you know! As Tables 14.4 and 14.5 show, we’re definitely on
the right track here. Waiting to enter until the open following the move that actually triggered the trade did little good. After a little experimenting, the profit and
risk factors are back to relatively high levels, at least for the long-only version. The
results for the both-sides version are still a little so-so, but the way it’s improving
gives plenty of hope.
Now, there’s only one more thing to address in regards to the entry and that
is the relatively small amount of trades generated. So far, the system has required
two lower lows in a row to enter on the long side. But what would happen if we
altered that rule a bit, to only require two lows lower than a third preceding low.
Will that increase the number of trades without ruining the results? Let’s try it.
Tables 14.6 and 14.7 show that not only did this modification more than double the number of trades, it even improved the results quite a bit—so much so, that
the risk–reward ratio for the portfolio traded on both sides now is above 1 (1.11),
which is very good indeed. Granted, this number is contradicted somewhat by the
TAB LE
14.4
Testing Short-term Risk–reward Relationship (1)
Long only, 3:1 risk–reward relationship, open excluded
PercProf: 81.54
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
60.85
18.89
38.91
9.21
21,953.83
30,078.20
377.95
510.36
3,226.06
Market
0.11
High:
Low:
79.74
41.96
48.12
29.71
52,032.03
(8,124.37)
888.30
(132.41)
3,604.01
(2,848.12)
Portfolio
0.74
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.39
0.20
19,873.20
16.87
5.77
3.88
St. Dev:
High:
0.51
1.90
0.27
0.47
12,016.79
31,889.99
11.29
28.15
3.13
8.90
1.75
5.63
Low:
0.88
(0.07)
7,856.41
5.58
2.65
2.13
CHAPTER 14
TAB LE
169
14.5
Testing Short-term Risk–reward Relationship (2)
Both sides, 3:1 risk–reward relationship, open excluded
PercProf: 64.62
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
115.15
34.97
35.31
7.09
14,542.14
39,415.20
254.39
356.10
3,022.69
Market
0.08
High:
Low:
150.12
80.18
42.40
28.22
53,957.34
(24,873.06)
610.49
(101.71)
3,277.08
(2,768.30)
Portfolio
0.71
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.15
0.33
1.49
0.82
0.08
0.21
0.29
(0.13)
26,899.76
16,040.17
42,939.92
10,859.59
22.43
15.27
37.70
7.16
10.06
4.94
15.00
5.12
3.58
1.54
5.12
2.04
Average:
St. Dev:
High:
Low:
low values for the lower one-standard-deviation boundaries for both the profit factor and the risk factor. But both the profit and risk factors are still good enough.
For now, however, we won’t care so much about the negatives, but instead
rejoice in the high risk–reward ratios for both the latest portfolios, and an everincreasing number of profitable markets. Another cool thing is that this latest version of the system, despite a much lower average profit per trade and shorter trade
length, actually nets more money than the original system. This can be estimated
TAB LE
14.6
Increasing Number of Trades Generated (1)
Long only, 3:1 risk–reward relationship, slightly altered
PercProf: 89.23
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
147.09
38.29
38.94
6.78
49,746.53
48,002.37
357.54
381.51
3,305.81
Market
0.10
High:
Low:
185.39
108.80
45.72
32.16
97,748.91
1,744.16
739.04
(23.97)
3,663.35
(2,948.27)
Portfolio
0.94
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.31
0.17
31,047.12
22.31
14.33
4.10
St. Dev:
High:
0.30
1.61
0.17
0.35
15,214.45
46,261.58
13.82
36.14
5.02
19.36
1.65
5.75
Low:
1.01
0.00
15,832.67
8.49
9.31
2.45
PART 2
170
TAB LE
14.7
Increasing Number of Trades Generated (2)
Both sides, 3:1 risk–reward relationship, slightly altered PercProf: 73.85
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
279.43
74.17
35.30
5.55
37,765.83
67,417.87
308.13
277.14
2,991.74
Market
0.10
High:
Low:
353.60
205.27
40.86
29.75
105,183.70
(29,652.04)
585.27
31.00
3,299.87
(2,683.60)
Portfolio
1.11
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.15
0.26
1.40
0.89
0.09
0.17
0.26
(0.08)
37,529.46
23,935.55
61,465.01
13,593.91
28.07
22.85
50.92
5.22
23.08
6.70
29.78
16.38
3.46
1.10
4.56
2.36
Average:
St. Dev:
High:
Low:
FIGURE
14.1
Citigroup traded using revised Harris 3L-R pattern—Winter 2001–2002.
CHAPTER 14
171
by multiplying the average number of trades per market by the average profit per
trade and market. For the original system, this value comes out to $64,750 (1,295
* 50), but with the latest version of the system, traded from both sides, the average net profit per market comes out to $85,932 (308 * 279). We will carry this version with us for further testing in Parts 3 and 4. Figure 14.1 shows a few sample
trades in Citigroup during the winter of 2001–2002.
TRADESTATION CODE
Variables:
AllowLong(True), AllowShort(True), PercentTarget(3), PercentLoss(1),
ProfitTarget(0), StopLoss(0), LongProfit(0), LongStop(0), ShortProfit(0),
ShortStop(0);
If BarNumber = 1 Then Begin
ProfitTarget = PercentTarget * 0.01;
StopLoss = PercentLoss * 0.01;
End;
If AllowLong = True and Low < Low[2] and Low[1] < Low[2] Then
Buy ("L-Nov 01") NumCont Contracts Next Bar on High[2] Stop;
If AllowShort = True and High > High[2] and High[1] > High[2] Then
Sell ("S-Nov 01") NumCont Contracts Next Bar on Low[2] Stop;
End;
LongProfit = EntryPrice * (1 + ProfitTarget);
LongStop = EntryPrice * (1 - StopLoss);
ShortProfit = EntryPrice * (1 - ProfitTarget);
ShortStop = EntryPrice * (1 + StopLoss);
ExitLong ("L-Stop") Next Bar at LongStop Stop;
ExitLong ("L-Trgt") Next Bar at LongProfit Limit;
End;
If MarketPosition = -1 Then Begin
ExitShort ("S-Stop") Next Bar at ShortStop Stop;
ExitShort ("S-Trgt") Next Bar at ShortProfit Limit;
PART 2
172
End;
End;
CHAPTER
15
Expert Exits
Originally presented in June 2002, the idea behind this simple swing trading system is to maintain profitability while keeping losses as small as possible. The basic
system is the same as that used in the risk control and money management articles
about finding the best exit level (Active Trader, March through June 2002).
When a market makes a lower high than the previous day’s high and closes
below the open (reverse the reasoning for short trades), the system identifies this
as a correction against the anticipated direction of the trade. Any market that has
fulfilled these two criteria at the open of the next day’s trading is a potential trading candidate.
On the day of the anticipated trade, the stock also needs to open below the
previous day’s high (above the previous day’s low, for a short trade). With the final
criteria in place, an order can be placed to buy a break above yesterday’s high
(below yesterday’s low).
The logic can easily be altered. For example, you could require the stock to
take out the high from two days ago, or the close to be less than the previous day’s
close rather than the same day’s open.
The entry strategy is accompanied by a 1 percent stop loss and a 4.5 percent
profit target. To avoid tying up money in trades that go nowhere, any open trades
are exited after eight days.
A trade-sizing model was added to the entry rule. The system trades fewer
shares or contracts when the market is more volatile. In such conditions, the trade
size is based on four times the average true range over the last 10 days, with a maximum risk per trade of no more than 2.5 percent of available equity.
173
PART 2
174
SUGGESTED MARKETS
Stocks, stock index futures, index tracking stocks (SPDRs, DIAs, QQQs), futures,
and currencies.
ORIGINAL RULES (REVERSE THE LOGIC FOR SHORT TRADES)
Yesterday’s high should be lower than the previous day’s high; yesterday’s close
should be lower than yesterday’s open; and today’s open should be lower than yesterday’s high.
Go long on a break above yesterday’s high.
Risk 2.5 percent of available capital per trade.
Exit with a loss if the market moves against you more than 1 percent.
Take profits if the market moves in your favor by more than 4.5 percent.
Liquidate any remaining trades after eight days.
TEST PERIOD
July 1992 to February 2002 (2,500 days of data per security).
TEST DATA
Daily stock prices for the 30 highest capitalized stocks in the NASDAQ 100. A
sum of $20 per trade has been deducted for slippage and commission.
STARTING EQUITY
$100,000 (nominal).
Unlike many other systems, this one trades the short side as well as the long—
a necessary criterion to keep the drawdown to a minimum during prolonged
downtrends, such as the one we’re currently experiencing. The system, in fact,
is in the midst of its worst drawdown since the start of the testing period, but so
is the NASDAQ 100 index; so far the system’s drawdown doesn’t come anywhere near that of the NASDAQ 100. Other than the recent drawdown, the system’s history has been very good indeed, as indicated by the drawdown chart
(not shown).
Note that the average time spent in a trade—1.6 days—is very short. This, in
turn, results in a low average profit per trade of $70. This may not seem much, but
remember that it is the average profit for all trades, including losers. The average
CHAPTER 15
Expert Exits
175
winner is larger, but because there’s only one winner for two losers, the average
profit per trade is affected.
Another important thing to remember is that this number also is highly influenced by many trades made at the beginning of the testing period, when the markets were trading at considerably lower levels. The average profit per trade in
today’s markets (in dollar terms) is considerably higher.
Nonetheless, this system is a good example of how a steady stream of smalldollar gains can accumulate significantly over time. Systems that profit in this way
can be considerably more profitable than a buy-and-hold strategy, or a trade
approach that shoots for the big bucks on every trade.
This system really doesn’t have any optimizable variables to work with, except for
the exit levels (which we will leave for Part 3) and the option to work with a trailing stop instead of a fixed stop loss. However, I decided to feature it here as an
example of a different testing methodology. The logic for researching the signals
in this system has already been discussed in Chapter 1. Therefore, I will only run
through it again very briefly.
During the initial testing of a system, we really shouldn’t concern ourselves
with the performance of the system, but rather the reliability of the signals it generates. To do that, you need to test all the signals generated, using standardized
stops and exits. Normal system testing usually only tests the first signal in a cluster of entry signals, assuming the others can be ignored because you would have
been in a trade already. However, whether you would have been in a trade or not
depends on your stop-loss and profit-taking levels and how long the trade should
last if none of these levels is hit.
Therefore, when researching a system, it’s important to look at all signals it
generates, so that it can be trusted just as much on its second or third signals as it
can on its first signal. For example, assume that you, for some reason, missed a
signal one day. The next day you get a new signal in the same stock, despite the
fact that you should have been in this stock already had you been able to trade. If
you haven’t done your research properly, you have no idea whether the second signal is likely to be as valid and reliable as the first one.
Look at Figure 15.1, which shows a chart of all signals this particular system
generated in Microsoft during the fall of 2001. It shows that in early August 2001,
two signals indicated to go short only one day apart from each other. In late October
and early November, two signals two days in a row indicated to go long. The point
is that, in either case, the second signal most likely would have gone unanalyzed,
because you already would have been in a trade generated by the first signal.
The same reasoning holds for the exit techniques as well. To make the most
out of the chart pattern and its exit techniques, you need to have done your
PART 2
176
FIGURE
15.1
Microsoft traded using original expert exits system—Fall 2001.
homework before you set out to trade the pattern in question and analyzed the
exits in such a way that they would work on average equally as well for all signals, no matter whether each specific signal would have been traded or not.
Therefore, the testing must be done in such a way that all signals will be tested
at one time or another, together with several different exit levels. To do that,
trade the system at random several times. (To learn more about this system and
how to test other systems the same way, see Active Trader magazine, February
2002 to June 2002.)
Once the system and all its signals are fully tested, using a random number
generator, the system can be tested according to normal principles. Table 15.1
shows the results for the system, as featured in the original article, when tested on
65 different markets. As you can see, it’s doing really well, with an average profit
per trade of $348, and profit and risk factors of 1.49 and 0.30, respectively. The
risk–reward ratio of 1.06 also is very good, and indicates that at least 84 percent
of all trading sequences will end in a profit.
CHAPTER 15
Expert Exits
177
TAB LE
15.1
Retesting the Original Expert Exits System
Original system, both sides
PercProf: 89.23
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
297.22
83.60
32.52
6.34
92,316.40
90,092.46
348.56
328.64
3,485.34
Market
0.09
High:
Low:
380.82
213.61
38.86
26.18
182,408.86
2,223.93
677.21
19.92
3,833.91
(3,136.78)
Portfolio
1.06
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.28
0.28
1.57
1.00
0.18
0.18
0.36
(0.00)
47,367.80
38,828.29
86,196.09
8,539.51
34.00
39.93
73.93
(5.93)
30.96
9.87
40.83
21.08
4.32
1.32
5.64
3.00
Average:
St. Dev:
High:
Low:
Tables 15.2 and 15.3 show how the original system performed on the long and
the short side, respectively. As you can see, the system is doing very well on the
long side: 93.85 percent profitable markets mean that 61 out of the 65 markets tested profitably, which is very good indeed. That the lower one-standard-deviation
boundaries for the risk and profit factors are well above one and zero, respectively,
confirms that this is a very robust system on the long side.
For the short side, however, the results are less tantalizing. It’s true the system is profitable overall, with a healthy 69 percent of the markets producing profTAB LE
15.2
Long-side Trading Using Original Expert Exits System
PercProf: 93.85
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
179.46
53.86
35.29
7.12
87,812.22
59,499.55
563.07
405.02
3,516.35
Market
0.15
High:
Low:
233.32
125.60
42.41
28.17
147,311.78
28,312.67
968.09
158.06
4,079.42
(2,953.28)
Portfolio
1.39
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.49
0.30
31,178.49
21.78
19.14
4.40
St. Dev:
High:
0.39
1.88
0.22
0.51
19,451.39
50,629.89
19.07
40.85
7.19
26.33
1.44
5.84
Low:
1.11
0.08
11,727.10
2.71
11.96
2.96
PART 2
178
TAB LE
15.3
Short-side Trading Using Original Expert Exits System
PercProf: 69.23
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
170.88
57.00
29.80
7.06
18,437.41
64,994.32
123.15
457.02
3,399.69
Market
0.03
High:
Low:
227.88
113.88
36.86
22.75
83,431.72
(46,556.91)
580.17
(333.88)
3,522.84
(3,276.54)
Portfolio
0.27
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.12
0.33
1.45
0.80
0.07
0.22
0.29
(0.15)
48,524.51
31,726.67
80,251.18
16,797.84
41.45
32.58
74.03
8.87
18.25
7.96
26.21
10.29
4.34
1.30
5.63
3.04
Average:
St. Dev:
High:
Low:
it, but most important numbers are a little on the low side. But is it really worth
trading it from both sides for the downside protection in case of prolonged downtrends, given the fact that the short side also decreases the overall and long-term
risk–reward relationship? This is a difficult question to answer, and something you
have to do for yourself, considering your own preferences. The question you need
to ask yourself is, “Am I willing to sacrifice some trading comfort (and profit) during normal circumstances, to be better prepared to make a profit (or at least scrape
by) during the downtrends?” If the answer is yes, you should trade the short side
as well; if it’s no, you should stick to the long side only.
Table 15.4 illustrates the robustness of this system, traded from both sides.
For Table 15.4, the random number generator (RNG) was left on and the system
tested 10 times each on all markets for a total of 650 test runs. Because the RNG
sometimes allows the system to enter into a trade, and at other times it doesn’t,
each trading sequence is unique and can consist of any and all of the signals generated. As you can see, this resulted in an even higher average profit per trade and
higher profit and risk factors than in the original system, tested the normal way.
Thus, only trading the first signal in a series of signals isn’t the most lucrative
thing to do. However, with additional profit potentials comes additional risk. With
a risk–reward ratio of 0.92, this version is slightly riskier to trade than the original
version. Lower one-standard-deviation boundaries for the profit and risk factors
confirm this observation.
One way to alter the original system is to substitute the fixed stop loss with a
trailing stop that, for example, exits a long trade if the market falls a certain amount
from the most recent highest high or highest close, or from the entry price immediately after the entry. All trades require a certain amount of leeway to be able to
CHAPTER 15
Expert Exits
179
TAB LE
15.4
Trading Both Sides Using RNG
Original system, both sides, random entries
PercProf: 86.92
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
165.06
49.54
32.77
7.02
52,947.82
57,816.14
375.55
409.49
3,469.47
Market
0.09
High:
Low:
214.60
115.51
39.79
25.75
110,763.96
(4,868.31)
785.04
(33.94)
3,845.01
(3,093.92)
Portfolio
0.92
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.31
0.34
1.65
0.97
0.19
0.21
0.40
(0.02)
34,605.77
22,807.03
57,412.80
11,798.74
26.90
22.76
49.66
4.15
17.52
6.70
24.22
10.82
4.36
1.34
5.70
3.02
Average:
St. Dev:
High:
Low:
survive the typical amount of noise in a market. Because you have no idea how
much leeway each specific trade will need, the best you can do is estimate an average leeway that seems to work best within each trade for a large group of trades.
For example, a trade with a profit target at 5 percent and stop loss at 1 percent (no trailing stop) has an average wiggle room of 6 percent, no matter how
long it lasts. If you use the same wiggle room for all trades, the average wiggle
room for all trades will also be 6 percent. If you replace the stop loss with a trailing stop, then the wiggle room within an individual trade that shows a profit will
become smaller with time. Therefore, to keep the average wiggle room constant,
within both an individual winning trade and all trades (both winners and losers),
the wiggle room must be slightly larger at the beginning of a trade with a trailing
stop than it must be for a trade with only a stop loss.
This creates a twofold problem: Not only will the largest single-trade loss for
a trailing stop be a little larger than that for a fixed stop (because the trailing stop’s
initially greater leeway means larger potential losses), but the best-case scenario—
the profit target—will also not be reached as often as before. This is because some
profitable trades that would have remained open if a fixed stop were used (and
therefore might have ultimately reached the profit target) will instead be stopped
out by the trailing stop. Another way to look at it is to understand that, for a profitable trade, the trailing stop will move in the direction of the trade to decrease the
chance for a profitable trade to go bad. Because it’s closer to the price than where
the fixed stop would have been had we used one, it will also be hit more often,
which leaves fewer trades to reach the profit target.
Thus, the profit target must be lowered for two reasons. Reason one is to
keep the average wiggle room constant, given that the trailing stop will create
PART 2
180
more wiggle room at the beginning of the trade, but less at the later stages of a
winning trade. Reason two is to increase the number of trades that reach the target, to maximize the profit potential when the trailing stop will make it easier for
a trade to exit with a less than maximum profit. However, sometimes the profit target will be increased instead of decreased. Still, however, more often than not,
despite the increased profit target, the initial risk–reward relationship going into
the trade will not be as favorable as with the same system using a stop loss. Most
often, the average profit per trade also will be lower when shifting from a stop loss
to a trailing stop.
Therefore, to be effective, a trailing stop must increase the number of winning trades so that the resulting system’s slightly smaller winning trade size makes
up for its slightly greater largest single-trade losses. A system with a trailing stop
can also increase profits further because, more often than not, it will shorten the
trade length, which results in more trading opportunities with a higher likelihood
of success.
Table 15.5 shows the result of a trailing-stop version of the system, with the
trailing stop at 1.6 percent away from the most recent highest high (lowest low in
a short trade) —which also is the initial worst-case scenario—and the profit target
at 4 percent. If you compare Table 15.5 with Table 15.1, you will find that all the
anticipated differences between the two versions also held true in the testing. For
one thing, the average profit is slightly smaller for the trailing-stop version, but
because the percentage winners and the number of trades are slightly higher, and
the trade length is a little shorter, the average net profits are almost the same. A
marginally higher risk–reward ratio for the trailing-stop version also indicates that
TAB LE
15.5
Using Trailing Stops
Trailing-stop version, both sides
PercProf: 87.69
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
316.60
92.40
41.24
5.68
90,239.93
87,191.48
329.24
308.19
3,007.20
Market
0.10
High:
Low:
409.00
224.20
46.91
35.56
177,431.41
3,048.46
637.43
21.05
3,336.44
(2,677.96)
Portfolio
1.07
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.36
0.20
43,673.54
31.76
26.44
3.46
St. Dev:
High:
0.37
1.74
0.20
0.39
40,969.57
84,643.11
41.42
73.18
8.99
35.43
1.15
4.61
Low:
0.99
(0.00)
2,703.96
(9.66)
17.45
2.31
CHAPTER 15
Expert Exits
181
TAB LE
15.6
Trading Long-side Using Trailing Stop
Trailing-stop version, long only
PercProf: 92.31
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
186.88
53.95
34.67
6.80
85,459.01
60,187.21
527.49
392.24
3,493.48
Market
0.14
High:
Low:
240.83
132.93
41.47
27.87
145,646.22
25,271.81
919.73
135.26
4,020.97
(2,965.99)
Portfolio
1.34
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.45
0.35
1.81
1.10
0.28
0.20
0.48
0.07
32,835.69
20,403.51
53,239.20
12,432.19
22.37
20.14
42.51
2.23
19.21
7.12
26.32
12.09
4.37
1.41
5.77
2.96
Average:
St. Dev:
High:
Low:
its trades are more similar looking than those trades generated by the original stoploss version of the system. Overall, it’s a matter of personal taste, given that the
average profit per trade needs to be large enough to warrant trading in the first
place. Table 15.6 shows the trailing-stop version of the system traded on the long
side only.
Table 15.7 shows how the trailing-stop version fared when trading the entry
signals at random. Comparing it first to Table 15.4, we can see that it too confirms
TAB LE
15.7
Random Entry Signals and Trailing Stops
Trailing-stop version, both sides, random entries
PercProf: 86.15
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
171.22
52.87
41.28
6.32
48,176.37
54,310.50
320.63
357.57
3,002.87
Market
0.10
High:
Low:
224.09
118.35
47.60
34.96
102,486.88
(6,134.13)
678.20
(36.94)
3,323.50
(2,682.24)
Portfolio
0.90
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.37
0.20
31,269.73
24.64
14.53
3.49
St. Dev:
High:
0.42
1.79
0.22
0.41
23,582.58
54,852.31
23.00
47.64
5.90
20.42
1.19
4.67
Low:
0.95
(0.02)
7,687.15
1.64
8.63
2.30
PART 2
182
our initial assumptions and the findings from Table 15.5. However, as opposed to
Table 15.4 in relation to Table 15.1, Table 15.7 shows both a lower average profit
per trade and a lower risk–reward relationship than Table 15.5, which suggests that
the trailing-stop version should be traded in a normal fashion on the first signal
only. One way to do it might be to trade the trailing-stop version as you’d do with
any system, and then add a trade every so often, which you monitor according to
the stop-loss rules.
TRADESTATION CODE
Variables:
AllowLong(True), AllowShort(True), RandomEntry(False), TrailingStop(False),
BarsInTrade(8), ProfitExit(4.5){4}, LossExit(1){1.6},
RandomTrigger(0), LongStop(0), ShortStop(0), LongTarget(0), ShortTarget(0),
Top(0), Bottom(0);
RandomTrigger = IntPortion(Random(2));
ProfitExit = ProfitExit / 100;
LossExit = LossExit / 100;
LongStop = 1 - LossExit;
LongTarget = 1 + ProfitExit;
ShortStop = 1 + LossExit;
ShortTarget = 1 - ProfitExit;
End;
Top = High;
Bottom = Low;
If (RandomEntry = False or RandomTrigger = 1) and MarketPosition = 0 Then
Begin
If AllowLong = True and High < High[2] and Close < Open and Open Next Bar
< High Then
Buy ("L-June 02") NumCont Contracts Next Bar at High Stop;
If AllowShort = True and Low > Low[2] and Close > Open and Open Next Bar
> Low Then
Sell ("S-June 02") NumCont Contracts Next Bar at Low Stop;
End;
CHAPTER 15
Expert Exits
183
If TrailingStop = True Then Begin
Top = MaxList(Top, High);
ExitLong ("L-Trail") Next Bar at Top * LongStop Stop;
End
Else
ExitLong ("L-Stop") Next Bar at EntryPrice * LongStop Stop;
ExitLong ("L-Trgt") Next Bar at EntryPrice * LongTarget Limit;
End;
If MarketPosition = -1 Then Begin
If TrailingStop = True Then Begin
Bottom = MinList(Bottom, Low);
ExitShort ("S-Trail") Next Bar at Bottom * ShortStop Stop;
End
Else
ExitShort ("S-Stop") Next Bar at EntryPrice * ShortStop Stop;
ExitShort ("S-Trgt") Next Bar at EntryPrice * ShortTarget Limit;
End;
If BarsSinceEntry = BarsInTrade + 1 Then Begin
ExitLong ("L-Time") Next Bar at Market;
ExitShort ("S-Time") Next Bar at Market;
End;
End;
{Code for testing robustness goes here (see Part 3 of book), with Normalize
(True). Set RobustnessSwitch(True).}
CHAPTER
16
Evaluating System Performance
Before we move on to Part 3, let’s make a few individual observations for all the
systems and a few more general observations.
The meander system had not done well after it was first featured in Active
Trader magazine, but because it was apparent that it still did a good job finding
many good trading opportunities, it was possible to put the performance on track
again, by letting the system ride the good trades for a little longer. This was possible because the original average trade length was very short in the first place.
Unfortunately, the system did not function that well on the short side when
using the same rules as for the long side. There probably are two major reasons for
this. First, a down move does not behave the same as an up move, which means
the initial risk–reward relationship going into a trade must be different from that
for a long trade. Second, the long version of the system operates with limit orders.
Because of the inherent upside bias in the stock market, it probably would be better to trade the short side using stop orders.
The expert exits system (Chapter 15) wasn’t really featured here to illustrate
a specific entry technique, but rather as a way of optimizing the stops and exits
over several different market conditions and markets. However, the entry technique is worth studying, because it works really well in its simplicity—at least on
the long side. A relatively low percentage of profitable trades can make this system difficult to trade for those of us who demand immediate positive feedback on
our trading.
As far as the average trade length goes, it could be argued that perhaps it is
a little too short, and perhaps we could make more of the winning trades by allowing them to go on for a little longer. If that were to happen, however, we must do
185
186
PART 2
so without letting the total time spent in a trade increase to a point where we limit
our diversification possibilities by being fully invested after only a few trades.
Even without the benefit of hindsight and the original trend filter, the
volume-weighted average system (Chapter 13) has held up well throughout the
long bear market, although a combined analysis of Tables 13.1 and 13.3 indicates
that the average profit per trade on the long side has decreased over the last several years while, at the same time, the average trade length has gotten a little shorter. Both these findings suggest that the thrusts to the upside are not as large and
forceful in a downtrend as they are in an uptrend.
The different lookback periods for the short and the long sides, given the
results in Tables 13.5 and 13.6, confirm that short-term down moves generally are
more explosive in nature than short-term up moves. Another, more philosophical
way to look at it, is that the shorter lookback period for the down side indicates
that a market discounts and then forgets bad news quicker than it does good news.
The RS system No. 1 (Chapter 9) is one of three systems that, later in the
book, will be used as a (trend) filter rather than as an outright entry trigger. As
such, it needs to have a slightly longer average trade length to open up a window
for the other systems to trigger an entry. However, because this normally also
means that the time spent in the market will increase, you have to be careful that
the system doesn’t spend too much time in the market and thereby make itself useless. In this case, the average trade length on the long side comes out to approximately 20 days.
With the time spent in the market at 70 percent, the system will spend an
average of about 10 days out of the market for every 30-day period. Putting this in
relation to, for example, the meander system, when using RS system No. 1 as a filter for the meander system, the long side of the meander system will decrease its
time in the market to approximately 30 percent and its number of trades per market to approximately 130. This still feels like a little too much for optimal diversification, but we will use these numbers to see what we can learn from them.
At first glance, the code for the relative-strength bands system (Chapter 11)
looks very complicated, with a lot of calculations and comparisons between markets. However, if you stop and think about it, it really isn’t all that difficult. All
we’re really doing is comparing the trend of several different markets—something
we do in our heads all day long anyway, at least if we also tinker around with the
more subjective kind of technical analysis. This is only a way to formalize it all,
so that we can digest more information from more markets. Nothing more, nothing less.
If for nothing else, one important thing we learned from this system was that
testing only on three markets doesn’t even come close to producing results that
will be reliable and robust in the long run. However, by expanding the research to
include several markets, we had enough observations to allow us some room for
tinkering with the system. As it turned out, this system was much better off get-
CHAPTER 16
187
ting rid of several of the original rules and input variables. With fewer variables
tested on more markets, the end versions of this system are much more likely to
hold up in the future.
In this case, we ended up with both a long and a short version of the system.
Both versions were profitable, but unfortunately this profitability also came at the
price of very volatile results, as illustrated by the low risk–reward ratios. For the
remainder of the book, this system will be used as a (trend) filter for the other
entry techniques, which should help bring down the time spent in the market by
approximately 50 percent for most of them.
If we thought that the code for the relative-strength bands system was complicated, then what must we think about the code for the rotation system (Chapter
12)? Again, it really isn’t that complicated at all. All that we’re doing is comparing the strength of the trend between several markets. But this time, instead of
looking at the distance between the relative-strength line and its moving average,
we’re looking at the slope of the moving average. This is very much like having
several charts in front of you, comparing them all with each other, trying to come
up with the chart that has the most strength and also is likely to continue strong in
the future.
Because the original version of the rotation system was tested in a way similar to the relative-strength bands system, we again had to expand the number of
markets tested to come up with statistically reliable results. This time, however, the
original results had held up much better since the system was originally featured.
However, because all markets were selected at random, the chance also exists that
the results from both of these relative-strength systems can be either better or
worse than a more thorough examination would reveal. The possibility for that is,
however, something most statistical examinations have to live with. The best we
can do is make the sample large enough to minimize the possibility.
Note also that I decided to change the logic for the short side halfway
through the research process—just like that—and without really starting the
research anew. Of course, the correct thing to do would have been to back up and
step through the entire research process again, but because we’re not using the
word “research” here in its most scientific form, but rather as a word for describing my thought process, I decided to just move on as if nothing happened. When
it comes to the entry techniques, I am not so much interested in coming up with
the optimal solution, but rather a solution that makes sense to me. Right or wrong?
We can argue about that later.
For the remainder of the book, this system too will be used as a filter for the
other entry techniques, which should help bring down the time spent in the market by approximately 50 percent for most of them.
The hybrid system No. 1 (Chapter 8) was one of the systems that held up best
over time. But, as was the case with many of the other systems, it did not fare that
well on the short side. Interestingly, it turned out that the best way to modify this
188
PART 2
system was to make it more aggressive than it was originally. More often than not,
when testing an old system on new data, the “best” way to improve it, or to curve
fit it to the previously unseen data (if we want to be really critical), is to make it
more difficult for the system to enter into a trade. The fact that we didn’t have to
do that this time is a good sign that this very basic entry technique does a good job
of identifying high-probability trading opportunities and that it will continue to
work in the future as well.
The two major disadvantages of the system, as of now, are that the average
trade length is about twice as long as we would want it to be, and the time spent
in a trade is way too long. We really need to get the time spent in a trade down by
something like 10 to 15 percent.
When revising the research on the Harris 3L-R pattern variation system
(Chapter 14), I found it had one major flaw built into it. This had nothing to do
with the original logic, created by Michael Harris, but was completely of my own
doing when adding the stops and exits to go with the entry technique.
However, when altering the exit rules, it also turned out the system traded a
little too infrequently. To come to grips with that, I had to make a few modifications, such as getting rid of trading on the open the day after the signal and not asking for two consecutive lows (highs) before the market turns and breaks higher
(lower). Because both modifications not only increase the results, but also relax
the criteria for getting into a trade, it is fair to say that this new version of the system actually is less curve fitted than the original one, and therefore also more
robust and more likely to hold up in the future.
As a general observation, it is evident that I have not done a particularly good
job of making these systems profitable on the short side. However, there are several reasons for that. First, when many of these systems were featured for the first
time in Active Trader magazine, the bear market wasn’t developed enough to test
the systems and, in many instances, I decided to make them long only because that
is what most of my readers are most familiar with.
In revising the research, I was stuck with the original idea and logic behind
the systems and, therefore, had to work with what I had. Maybe, just maybe, I
could have done a better job with the short side as well, had I been able to start
from scratch. Granted, some of you still might say that I could have done a better
job with what I had, but the question is, how far should I have taken the research
to do so? Sure, I could have indulged in more testing and optimizations, but I have
other topics that I need share with you as well. The purpose behind all this is to
give you a glimpse inside my head while I work with different system concepts for
Active Trader magazine, so that you can go out and do a better job yourself. I can’t
provide you with the definitive answers, because there are none.
Another important observation is that many of these systems are quite complex in their nature, which contradicts what I wrote in Trading Systems That Work,
that I like simplicity, and that preferably a system should not have more than three
CHAPTER 16
189
rules or calculations. Clearly, many of these systems have more rules than that. I
still stand by that rule of thumb, although I have to admit that I have relaxed it
quite a bit at times—obviously. If for nothing else, one simple reason is that it is
very hard to come up with system ideas to test every month. I apologize for this,
but hope that you will still be able to take the concepts as such, run with them, and
perhaps boil them down to something that will fit the three-rules rule as well.
Also, many of the systems seem more complicated than they really are. This
is especially true for the relative-strength systems that compare several markets
with each other. But all we’re really doing is formalizing something most of us are
trying to do in our heads all the time anyway.
Finally, I’ve already mentioned that I really don’t regard the exits as part of
the systems’ rules. In a little while, we will get rid of most of them completely and
substitute them for a new set of expert exits, developed individually for each system, just as we did in the experts exits system. Enough said. These are the systems
we will work with for the remainder of the book.
PART
THREE
Stops, Filters, and Exits
I
n this part of the book, we will look at various ways of adding stops and exits to
our entry techniques. If the preceding chapters were basically a demonstration of
how system development is more of an intuitive art form than a science, where you
rely more on your own gut feel and mental picture of what you want the system to
do, this part will be more scientific in nature. Here we only rely on what the hard
cold figures tell us, and we will be as precise as possible, without losing track of
the fact that the system needs to work as well in the future as it has in the past.
If you compare the final system with a painting representing reality, in Part
2, we applied the paint in broad strokes and perhaps even in a cubistic fashion,
leaving a lot to the interpreter to figure out what we want the system to represent
and do. In this part, we use a much smaller brush and try to paint in as much detail
as possible and in as realistic a fashion as possible, without forgetting that we can
never be 100 percent scientific or precise; we always leave a little piece of artistic
freedom in there. Otherwise, the system would work perfectly in the past, but not
at all in the future. Although we strive to be as precise as possible, it is that little
piece of artistic freedom and how we interpret things that sets us apart from other
painters (system builders) and assures our future success.
CHAPTER
17
Distribution of Trades
I don’t know how many articles and seminars I have read and listened to that
stressed the importance of keeping your losses short. Many of them illustrated with
figures like Figures 17.1 and 17.2, which show the distribution of a set of trades
before (Figure 17.1) and after (Figure 17.2) a stop loss has been applied to the system. In both figures, each column represents a number of trades ending at a certain
profit or loss. For example, the tallest column in both figures tells us that this system had 17 trades that ended with a profit of three units (dollars, cents, apples,
whatever—it doesn’t matter at this point). Also, note in Figure 17.1 how the distribution of the trades resembles the classic bell-shaped normal distribution.
As you can see, Figures 17.1 and 17.2 are essentially the same. The only difference is that a few trades have been taken away from the losing end in Figure
17.2. In Figure 17.1, the average profit per trade comes out to 2.8 units. In Figure
17.2, the average profit per trade is 3.31 units. Thus, the logic behind many of the
articles I’ve read and seminars I’ve listened to is that by cutting the losses short,
we can increase the profit per trade considerably (in this case by close to 20 percent). Or can we? Before you read any further, look at Figure 17.2 for a while and
try to figure out what’s wrong with it.
Can you see it? What’s wrong is that the largest losing trades are missing
completely, as if they were never made in the first place, which they must have
been. To get it right, we need to add those large losers from Figure 17.1 to the column representing the number of largest losers in Figure 17.2. If we do that, the
result will be as shown in Figure 17.3. If you compare Figures 17.2 and 17.3, you
will notice that the leftmost column is taller in Figure 17.3 than it is in Figure 17.2.
With these trades prudently added back to the sample of trades, the average prof193
FIGURE
17.1
Distribution of trades before use of stop loss.
FIGURE
17. 2
Distribution of trades after use of stop loss.
194
CHAPTER 17
195
it for all trades comes out to 2.94, which is considerably less than the 3.31 units
from Figure 17.2, which made it so easy to believe.
But that isn’t enough. Plenty of other things are wrong here that we still need
to address. Let’s take a close look at Figure 17.3 and try to figure out what we need
to address next.
Can you see it? What is wrong is that Figures 17.2 and 17.3 look exactly the
same with the exception of the leftmost column. This would not be the case in reallife trading. Instead, several of the trades that ended up as winners in the system
without a stop loss, would end up as losers. In the system without the stop loss, all
trades could fluctuate as they wanted until they got stopped out for reasons other
than having reached a certain maximum allowed loss. Several of those winning
trades would also have fluctuated, one or several times, around the stop-loss level,
which wasn’t in effect. But with the stop loss in effect, a trade can only touch this
level once and it is stopped out. There would be no second chance for that particular trade to prove itself and turn a profit. Instead, once the stop is hit, that trade
is out with a loss, and it is moved from its column in Figure 17.1 to the maximum
loss column in Figures 17.2 and 17.3.
FIGURE
17. 3
Adding in the largest losing trades.
PART 3 Stops, Filters, and Exits
196
For these particular charts, all trades were generated using Excel’s randomnumber generator, and there is no way to tell exactly which and how many trades
would have been exited above the stop loss, had it not been in place. Therefore, for
demonstration purposes only, I lifted a few trades off the other columns and added
them to the maximum loss column. The result can be seen in Figure 17.4. For good
measure, I also placed one trade to the left of the maximum loss column, as there
always will be a few trades that slip through the safety net (the stop loss), for one
reason or another. With the distribution looking like that in Figure 17.4, the average profit per trade now comes out to 1.89 units, which is more than 30 percent
less than the original results in Figure 17.1, and more than 40 percent less than in
Figure 17.2, where most other writers and seminar speakers would have left you.
That is, thanks to the stop loss, we are now making less money per trade than we
did originally.
Considering that we are now making less money than originally, if you compare Figures 17.3 and 17.4 would you say that I took away too many profitable
trades and added them to the maximum allowed loss column? Well, I don’t know
what you think, but I believe I most likely didn’t. Specifically, I believe I didn’t
move enough of the largest winners. For a trade to become a large winner, it needs
FIGURE
17. 4
Adding to the maximum loss column.
CHAPTER 17
197
volatility. But because volatility works both ways, without the stop loss, some of the
large winners actually started out as large losers. Therefore, with the stop loss in
place, a few of the would-be large winners would have ended up as small losers.
The same reasoning also holds true if we were to add a profit target. In that
case, all trades above a certain profit would have ended up no larger than what the
profit target would have allowed. But there also would be a few trades that originally ended up with a profit below the profit target, after they’ve had an open profit above it, which now will end up at the maximum allowed profit column. This is
depicted in Figure 17.5, whose distribution of trades shows an average profit of
1.95 units. This is slightly more than in Figure 17.4, which doesn’t always have to
be the case.
Note that the numbers here were generated at random and that the actual
numbers will, of course, vary with the system, but the general relationships
between the different stages of the research process always hold true, no matter
what. Also note that just because the average profit per trade decreased by more
than 30 percent from Figure 17.1 to Figure 17.4, it doesn’t mean that the system
behind the results in Figure 17.4 will be less profitable in the end. Quite the contrary. Because the stop loss also narrows down the possible outcomes for the
FIGURE
17. 5
Maximum allowed profit.
198
trades, the standard deviation of the returns will also decrease. Thus, the system
will be less risky to trade, and consequently you can dare to take a larger position,
which in the end might result in a larger profit than what would have been the case
with the original system.
Note also that the profit target in Figure 17.5 actually managed to increase
the average profit per trade and decrease the standard deviation of the returns at
the same time. Although this is not very likely to happen in a real system, it is a
possibility that only proper research and trade management will give you. Yet
another reason why a system with a stop loss and a profit target might be more
profitable than a similar system without those features, and despite a lower average profit per trade, is that the shorter trade lengths will make it possible to trade
more often on more markets.
As a final observation, note that we have taken a set of close to normally distributed trades and turned them into a distribution with a few very distinctive outcomes and a few trades scattered in between. That is, adding a set of thoroughly
researched exits, such as a stop loss and a profit target, makes it possible to calculate exactly what to expect from each trade in precise quantitative terms, instead of
just “knowing” that each trade can either be a winner or a loser ending up somewhere within the normal distribution curve. More important, however, is that the
end result of your trading becomes a function of your skills as a trade manager,
instead of random market fluctuations. And you don’t want your trading results to
be a function of randomness, do you? Let’s state that a little differently: If the outcome of your trades resembles the bell-shaped normal distribution curve, most likely the outcome of your trading (no matter if you’re a winner or a loser) is a function of randomness and can be explained only as good or bad luck, instead of skill.
Now, we could stop here and conclude that it pays off to do the homework
and think about a problem all the way to its end. But have we thought about it all
the way to the end? No, we haven’t. The truth is, we haven’t even started. In fact,
all we’ve just learned is wrong for one very specific reason: Every time we make
a change to a system, no matter how small it is, we change its characteristics and
need to start the research all over. For example, when you add or change your stop
losses and profit targets, the trade length of several of the original trades will
change as well. Most likely, adding a profit target and a stop loss will shorten the
trade length. And shortening the trades means that we free up money and markets
that otherwise wouldn’t have been available for trading, which will produce a completely new set of trades that needs to be added to the mix.
For example, consider a system without a stop loss and profit target that
enters into its first trade, which then lasts for 10 days. Then nothing happens for
another five days before the system enters into a new trade that lasts for eight days.
Now take the same system, with the same entry rules, but add a stop loss and profit target and do the research again. Now the first trade only lasts for five days
before it is stopped out. Then two days of no trading occur before the system enters
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199
into a new trade that is still open on the day the second trade started in the original system. Note that the second trade in the latter version of the system is possible because a signal that day went unnoticed by the original system because it was
in a trade already. The second trade in the latter version of the system then is
stopped out after 10 days, which would have been while the second trade in the
original system still remained open.
From this simple example, it is already easy to see that although the original
entry and exit rules are the same for the two system versions, the stop loss and the
profit target added to the second version make it a completely different system,
with a completely different set of trades. Therefore, when experimenting with a
system, you always have to do the research from scratch for every little change you
make. You still can work according to the general plan outlined by Figures 17.1 to
17.5, but you have to remember that for every little change you do, you might end
up with a completely new set of trades, with their own combined characteristics,
forming the characteristics of the system.
This also hints at another important consideration: A real-life track record is
worth nothing in this case, since you cannot do this research on a set of historical
trades that you might have generated in real life. This is because a lot (if not all)
of those trades would not have happened in the way suggested by the changes you
make during your research. Instead, you only can do this with hypothetically generated make-believe trades, because that’s the only way you can track and make the
most out of all the changes you make to the system and arrive at the robust solution you’re looking for.
To add extra reliability and robustness, you could do your testing according
to the principles outlined in Chapter 15, where we looked at a method for testing
the signals and the individual trades rather than the system itself. There, each trade
was traded at random and completely separated from the other trades generated
during the same test run. This can be done without renouncing any of the principles we’ve learned about in this chapter. We will try to use all that we have learned
so far in this chapter when we look for the optimal stop and exit levels for all the
systems described earlier. First, however, we need to learn how to examine the
data, which we discuss in Chapter 19. But first, let’s talk about why and how to
exit a trade in the first place.
CHAPTER
18
Exits
Basically, there are four major reasons to exit a trade:
■
Limiting a loss
Taking a profit
End of event
Money better used elsewhere
■
■
■
Let’s take a brief look at each one of these reasons and when they should be
used.
LIMITING A LOSS
I recently participated as a speaker in a seminar, where I asked the other participants which was the most common reason to exit a trade. About two-thirds of them
said taking a profit or cashing in on a good trade. Only one-third immediately said
that the stop loss probably was the most common reason. From what you know
about trading, which one of the two groups do you think is right?
As far as I know, it is group two, which said the stop loss. Just take a look at
the systems we worked with in Part 2. None of them has more than 50 percent
profitable trades, which means that a majority of the trades are exited with a loss,
and logic has it that’s the only way it could ever be. Think about it: When you enter
a trade, you might have a slightly better than 50 percent chance that the trade will
go your way, but because you also need to look for a risk–reward relationship of
about 3:1 to make the trade worth the risk you’re assuming, there is still a much
larger likelihood that the market will move against you by one unit (or 1 percent,
201
202
or 1 dollar, or whatever) than with you by three units (percent, dollars, etc.). Call
me a bad systems developer, but I believe there is no way around this sad fact.
To be fair to the group that first mentioned taking a profit as the most common exit reason, it didn’t take them long to change their opinion after they reasoned about it among themselves for a while. It’s still scary, though. Taking a profit still was the first thing that came into their minds when asked, and taking a profit probably also is the first thing that comes into their minds when entering a trade
in real life. Conditioning yourself to believe most trades will be profitable simply
can’t be the best way to prepare yourself to take that inevitable loss that will happen more often than you care to think about. (I know, this contradicts what I’ve
said previously: Why enter into a trade in the first place if you don’t think it will
be a winner? But such is your life as a trader, full of contradictions and “sure
things” that don’t turn out as they should.)
I also believe that not being prepared to take the loss right away makes us
take the loss for the wrong reason once we do take it. How many of us haven’t,
for example, done a trade like this: You enter the market believing this trade will
be a sure winner, only to find it moving against you right off the bat. After a
while, it also has passed through the level where you originally had decided to
take a loss, but because you were so conditioned to think this trade was going to
be a winner, you just can’t make yourself take the loss. Not until you have an open
loss twice the size that you were originally prepared to accept does the market
turn around and start trading your way. But before the trade starts to show a profit, the market stalls and trades sideways. After having watched the market move
sideways for quite some time, frustrated, you finally decide to get out of the trade
with a small loss.
What happened here? In the end, you did manage to end up with a smaller
loss than originally accepted, but was it worth it? For one thing, do you know how
many trading opportunities in this or other markets you missed because you had
your money and your attention focused on this trade? Probably not. Perhaps you
would have been better off taking the loss right away, so that you could have
entered this or another market a second time a little later. In that case, the frustrating sideways move might have come in a situation where you actually had a
small profit. Then you would have been in a much better position to just wait it
out, which you couldn’t do this time. And last but not least, didn’t you end up exiting a trade with a loss, even though it, in essence, finally went your way? There
was a sideways move going on, but hadn’t the trend reversed earlier? Yes, it had,
and I believe that taking a loss in this way is probably the most common exit there
is. It’s good to take a loss, but not for all the wrong reasons.
Consequently, the best and most efficient way to end a losing trade is with
a stop loss that preferably should be in place the second after you’ve entered
the market. This is also necessary for money management purposes, which we
will talk more about in the next chapter. Here, I only state that, if you have a well-
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working system, money management will make more of your bottom line than the
actual entry and exit rules themselves.
TAKING A PROFIT
I don’t know about your trading habits, but taking a profit is not the most common
reason to exit a trade in any of my systems. I wish it were, but I’m afraid it never
will be.
In my opinion, only two ways exist to take a profit. Technique number one is
to work with a profit target that lets you exit with a limit order. Technique number
two is to work with a trailing stop that moves in the direction of the trade, trailing
it at some specified distance. A trailing stop is probably the most common technique to exit a longer term trend-following trade. However, a trailing stop can also
result in a loss, depending on how the trailing stop is designed and if it also can
operate as a stop loss during the initial stages of a trade.
However, a trailing stop might not be the best way to exit a short-term trade
with a trading horizon of around three to ten days. All trades need a little wiggle
room, or leeway, to cope with the typical amount of noise in the market: Because
you have no idea how much leeway each specific trade will need, the best you can
do is estimate an average leeway that seems to work best for a large group of trades
and within each trade. We will do this shortly for our systems.
For example, a trade with a profit target at 5 percent and stop loss at 1 percent (no trailing stop) has an average wiggle room of 6 percent no matter how long
it lasts. If you use the same wiggle room for all trades, the average wiggle room for
all trades is also 6 percent. If you substitute the stop loss with a trailing stop, then
the wiggle room within an individual trade that shows a profit will become smaller with time, and sometimes the wiggle room will become too small and have you
stopped out of trades just moments before the market is about to take off in your
direction. If you work with a profit target, you might also have to place the target
closer to the entry price if you work with a trailing stop than you would had you
only worked with a stop loss. Because of the large wiggle room, some profitable
trades that would have remained open if a fixed stop loss were used—and therefore
might have ultimately reached the profit target—will instead be stopped out by the
trailing stop. To increase the number of target hits when using a trailing stop, the
target needs to be placed closer to the entry. This limits the profit potential even further when compared to the stop-loss version of the system, but increases the profit
potential for the trailing-stop version (when examined by itself), because more
trades will be exited at a maximum profit instead of a trailing stop.
But that isn’t all. To keep the average wiggle room constant over time, both
within an individual winning trade and all trades (both winners and losers), the
wiggle room also needs to be slightly larger at the beginning of a trade with a trailing stop than it needs to be for a trade with only a stop loss.
204
To be effective, then, a trailing stop must increase the number of winning
trades so that the resulting system’s slightly smaller winning trade size makes up
for its slightly greater largest single-trade losses. In the best of worlds, a trailing
stop can increase profits further because it shortens the trade length, which results
in more trading opportunities with a higher likelihood of success. But this will not
work at all times, because shortening the average trade length might demand a
longer maximum allowed trade length, to keep the average trade length within
desirable limits. As you can see, this is a complex matter and, depending on your
trading horizon and entry technique, it might be impossible to fit a trailing stop
into the equation.
END OF EVENT
Whatever chart pattern or indicators you’re using to enter a trade, some sort of
news or other fundamental event is usually behind the technical formation that
triggers the entry. Whenever we’re entering a trade, we need to be aware of this
event and ask ourselves at the end of the day exactly what that event was and if it’s
likely to play a role in the stock’s future development over the next several days.
Can you remember what type of fundamental news it was that made you buy and
sell today? Can you remember what it was yesterday or two days ago? Are those
reasons still valid, and is the market still talking about them? You probably can
remember these things and the reasons probably are still valid.
But can you remember what drove the market 10 or 15 days ago? Are those
factors still making the headlines? They probably aren’t, and most likely you can’t
remember what they were without looking in an old newspaper. Thus, a majority
of those reasons to be in a trade are no longer valid. The market has moved on to
discount other things, and so should you. In fact, I believe this is one of the most
underestimated reasons to exit a trade.
The difficulty with the end-of-event exit, however, is that it is very difficult
to measure and research. Most often, you have to implicitly assume the event is
over, based on other pieces of evidence the market gives you. For example, if you
measure how the market behaves one to several days after an entry signal, you
might find that after a certain number of days, the results, or the many different
paths the market can take, become more widespread or dispersed. Maybe a majority of your trades still move in the right direction, but those that don’t start to stick
out more. This is an indication that other pieces of news have hit the market and
that the market now prefers to discount that news instead of whatever piece of
news was behind your trade.
As we all know by now, the more widespread the outcome, the more volatile
the market, and the more volatile the market, the riskier it is. The more widespread
the different outcomes, the higher the standard deviation in relation to the estimated profit from the trades that are going your way. Sooner or later, there comes
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a point when the risk outweighs the diminishing reward for being in the trade. That
is when you should exit and ready yourself to trade the next event. Most of my
research on the NASDAQ stocks indicates an optimal maximum trade length of
five to nine days, depending on the entry technique.
Working with end-of-event exits also seems to produce the best results
together with breakout-type entries. This is pretty obvious, because breakouts are
the type of patterns most likely associated with some type of news fueling the market and creating the swift move needed to create the breakout. Swing trading patterns also can work well with an end-of-event stop. Usually, however, the swing is
a pattern that forms in several stages, with the final stage occurring some time
after the news first hit the market, which means the trade will usually be triggered
one or two bars after the breakout trade. This is not a watertight rule, however, and
sometimes the swing will trigger the trade before the breakout does—especially if
the market is anticipating something in the works for the stock in question.
Measuring the end of an event in units of time isn’t the only way to do it.
Another way is to measure how much the market is likely to move after a certain
entry is triggered. For this to work, you need to have researched how far the market is likely to move, on average, after an entry signal is hit. With this information
at hand, you can place a profit target this distance (and sometimes plus one or two
standard deviations) away from the entry. If and when this profit target is hit, you
know the market has done a better than average job of discounting the news that
fueled the move, and you can exit with a decent profit before the market realizes
it has done too good a job and starts to fall back to its starting level. Using this
logic, the end-of-event exit also functions as a profit target.
Many might argue that the above scenario is instead a good opportunity to
add to the trade. That might be so, and I haven’t extensively researched that possibility. The way I see it, however, is that the later in a move you enter into a trade,
or if you scale in, the greater the chance that that last entry will result in a loss.
Better, I think, to exit with a decent profit and prepare yourself for the next signal
with the same odds for success as the first one, in either the same or any other
market. Why tie up capital in a trade with ever decreasing odds for a continuous
profitable development? This conveniently brings us to the next reason to exit a
trade.
MONEY BETTER USED ELSEWHERE
What do we do when nothing happens? We have just entered the market, and the
trade is going nowhere. This is an especially important question for those of us
whose funds are limited. Maybe our entire capital is tied up in one or more trades
like this and, as long as it is, we’re really not monitoring the market for other trading opportunities. Thus, even though this specific trade is going nowhere, it is still
costing us money because it keeps us from entering into other trades. Where, how,
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and when do we decide that we should get out and ready ourselves for another
trading opportunity?
As is the case with the end-of-event exit, the slow-trade exit also can be
based on some intermediate target in time or price. For example, if the trade hasn’t moved into positive territory or reached a certain profit after one quarter or one
third of its expected life span, it could be cut. Had we kept it open, it might have
taken off eventually, but so can any other trade we can enter with the money from
this one. And while all other future and so far untaken trades haven’t proved themselves in any way, at least this one—the slow one we’re just about to exit—has
proved itself exactly that: a slow one. Consequently, you probably stand a better
chance entering into another market instead, or exiting and waiting for a new entry
signal in this market. In a short-term system, you could use the slow-trade exit the
same way as the end-of-event exit. If the event behind the move hasn’t proved itself
within the time frame during which it should have done so, then it’s time to exit no
matter the outcome.
This is also an important question to ask if you’re a more long-term trader
having trades lasting longer than a month. Many traders miss the fact that, when
they try to get as many profitable trades as possible, many times it is more important to get as many profitable time periods, such as months or quarters, rather than
profitable trades. Staying in a trade that is going nowhere or is losing money at a
slow but steady rate without hitting the stop loss, might weigh down your results
for several months in a row. As in the case of a more short-term trade, it also keeps
you from using that money in another trade that might have been more profitable.
Another way to watch for slow trades is to monitor and analyze volume and
open interest (in the futures and options markets). Measuring the relative strength
between different stocks or markets also could be a good idea. Perhaps you simply are trading the wrong stock in a group of similar stocks? These alternative
methods could also be used for the end-of-event exit. For this book, however, I will
only look closer into a few time-based techniques.
CHAPTER
19
Placing Stops
Basically, two ways can determine where to place a stop, both in relation to the
entry price and in relation to the current price of the market. Furthermore, there
also are two very wrong ways of doing this. Unfortunately, these two very wrong
ways also are the most commonly used methods. Therefore, let’s talk briefly about
the very wrong methods before we move on to the two methods we will use for the
remainder of this book.
Wrong method No. 1 is to assign an arbitrarily chosen dollar value to stocks
trading within a certain price range. For example, I recently was asked to test a
system that had assigned a $2 trailing stop to stocks trading within the $5 to $10
price range, a $3 stop for stocks trading between $10 to $20, and so on. For stocks
priced over $50, the system called for a 10 percent trailing stop.
Thus, for a stock trading at $5, the system developer thought it was wise for
you to risk 40 percent (2 / 5 0.4) of your invested capital in one trade, but “only”
10 percent for stocks priced above $50. Why? What’s the reason for this discrepancy? True, lower-priced stocks at times can be more volatile than higher-priced
stocks, but does this justify taking a 300 percent (40 / 10 1 3) larger risk in
the low-priced stock? If so, will the profit potential be 300 percent greater as well?
Nobody knows, and no matter what, allowing a trade to move against him by 40
percent is not the hallmark of a good trader. Heck, allowing a trade to move against
him by 10 percent isn’t the hallmark of a good trader, either.
Even within the same stock-price bracket, the difference in risk is as much
as 100 percent [(2 / 5) / (2 / 10) 1 0.4 / 0.2 1 1 100%]. And what
about those stocks that fluctuate back and forth between two brackets? For a stock
fluctuating around $10, for example, the risk could either be 20 percent (2 / 10 207
208
0.2) or 30 percent (3 / 10 0.3), which is a difference of 50 percent (20 / 30 1
0.5). Should you change in the middle of a trade?
Furthermore, assuming there is something to the logic behind this method,
still not everything is what it seems to be. Just because a stock seems to have been
priced around $5 way back when, that most likely wasn’t the case at the time. Take
Microsoft, for example. Looking at any chart updated today it seems as if the stock
traded at $5 in 1993 to 1994. But the only reason why that seems to be the case is
because the stock has been split several times, and the historical price has been
adjusted down. In real life, in 1993 to 1994, Microsoft traded around $80. And
even though the price has been adjusted down, the behavior is still baked into the
historical bars. This reasoning is also closely related to what we said about splitadjusted prices in Chapter 2.
Also, in the case of Microsoft and other highly liquid and highly traded
stocks, I doubt the behavior will change that much, no matter the actual price.
Consequently, the best you can do when back testing a system is to treat every
stock the same all the time and exactly as all other stocks, no matter the price. This
method doesn’t do that, and even though it might have its merits, it is not the best
way to go for back testing robust trading systems.
Wrong method No. 2 takes less explanation to dismiss. This method states
that you should never risk more than a specified amount of your trading capital in
any trade. For example, in the commodity futures markets, many system vendors
recommend that you should not risk more than $2,000 on any trade. What is that
all about? While it is prudent not to risk too much, the market doesn’t give a hoot
if you can’t afford to risk more than a specified amount on each trade. Instead, the
market will do what the market will do, and if you can’t adjust your maximum
allowed loss to the conditions that the market gives you, then the prudent thing to
do is not to trade. Period.
As already mentioned in Chapter 1, depending on the market value of the
market and the long-term trend, the effect of such a stop is that it will have you
stopped out time and time again on a high-priced market, but hardly ever on a lowpriced market. It will be too tight for the high-priced market, but too wide for the
low-priced market, in relation to the respective markets’ normal price swings.
Therefore, this system design blunder also can result in two opposite types
of drawdowns (or at least unwanted system characteristics), both of them very
hard to detect because they’re masking each other. In the case of the low-priced
market, a larger than necessary drawdown can be a result of a few but larger than
necessary losers, while in the case of the high-priced market, a larger than necessary drawdown can be a result of a large amount of unnecessary small losers.
Not knowing this, you might only worsen the effects from one type of drawdown
while addressing the other. Stick to a strategy like this and you will be broke
before you can say honorificabilitudinitatibus (the longest word ever used by
Shakespeare).
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PERCENT STOPS
The percent stop method is the more straightforward of the two correct methods
used in this book. Simply put, it places the stop the same relative distance away
from the entry point, no matter the price of the stock. For example, a 10 percent
stop should be placed $1 away from the entry price if the entry price is $10, but
$10 away from the entry price if the entry price is $100.
To calculate what a percentage-based stop means in dollar terms for a specific stock, simply multiply the price of the stock by the fractional value representing the percentage value. For example, because the fractional value for 5 percent is equal to 0.05, a 5 percent stop on a $60 stock should be placed $3 away
from the price of the stock (60 * 0.05 3).
To calculate how many percentages a certain dollar-based stop represents on
a certain stock, divide the stop distance by the price of the stock, and multiply by
100 to transform the fractional value to a percentage value. For example, if you use
a $6 stop on an $80 stock, the stop is 7.5 percent away from the entry price (6 / 80
* 100 7.5).
The last example was deliberately chosen so that I can refer back to the
Microsoft example. If it just so happened that you used a $6 stop on Microsoft
back in 1993, then you need to use a 38 cent stop (5 * 0.075 0.375) if you would
like to back test the system you used then on the same data as you used then: What
once was actually priced at $80 now seems to be priced at $5, and to make your
system behave the same, you need to adjust the stop so that it reflects the splitinduced changes in the price.
The main advantage of the percentage-based stop is that it works equally as
well, on average and over time, over a large number of stocks and different markets, no matter each individual market’s price at the time. Another advantage is
that it doesn’t need any new optimizable variables for its calculations. True, the
actual percentage values are optimizable, and the most optimal values will change
over time and vary from one stock to the next, but with a large enough sample for
testing, you will find the values that work best on average, around which the everchanging most optimal values will fluctuate.
The main disadvantage of the percentage-based stop is that it’s rather static
in nature and very seldom will it be the perfect stop for any individual trade. It
implicitly assumes constant market volatility, equal to the volatility that works the
best with whatever stop settings are in question. But because the volatility never
remains the same, and the changes only can be observed in hindsight, the percentage stop will only be almost perfect almost all the time. When it isn’t, it’s usually because the volatility is too high or too low.
If the volatility is too low, none of the stops and exits will get hit and the trade
will linger in no-man’s land for as long as the maximum allowed trade length
allows it to. This might result in several small losses and profits, with the profits
210
perhaps not even making up for the costs of trading. If the volatility is too high,
all stops and exits will be hit too soon, which will result in a higher than normal
amount of losing trades, and winning trades that aren’t as large as they could have
been, given the momentum created by the volatility.
The same two things can go wrong with the fixed-dollar stop just described.
The differences lie in the fact that the efficiency of the percentage stop will vary
rather quickly over time as the volatility fluctuates, and this error is not dependent
on the price or current trendiness of the market, as it is for the dollar-based stop.
Thus, in using a dollar-based stop, we’re making a systematic error that might
compound and worsen over time, which will not be the case for the percentagebased stop. Instead, only the short-term efficiency of the short-term stop will vary,
while the long-term efficiency is more likely to remain constant.
VOLATILITY
Unfortunately, while volatility can be observed all the time, it can only be measured in hindsight. But if you’re prepared to work under the assumption that the
most recent volatility also is a good indication of the volatility in the immediate
future, then you can replace the percentage-based stops with a set of more dynamic stops based on the current market volatility.
If you do, you have to remember that the volatility also must be measured so
that it becomes universally applicable on all markets. Basically, there are two common ways to do that. The first way is to calculate the moves from one close to the
next, measured in percentage terms, and then calculate the standard deviation of
the price swings. This method is most commonly used in the academic world and
by options traders, who use it as a part of an options-evaluations formula, such as
Black–Scholes, to calculate the fair value of an option. (Options traders use a logarithmic scale, but in essence, it’s the same thing.)
Using this formula, the larger the swings, the larger the standard deviation
and the further away the stops and the exits can be placed from the entry price to
avoid being stopped out too early. For example, by placing the stop one standard
deviation away from the entry price, only 16 percent of all price moves should
reach the stop. If the stop is placed two standard deviations away from the entry
price, only 2.5 percent of all price moves should reach the stop. Whatever you
decide, the distance between the entry price and the stop will remain constant in
standard deviation terms, but vary in percentage terms with the most recent market action. (Note that this is not the same as to say that only 16 or 2.5 percent of
your trades will be stopped out. There still is a 50–50 chance for the trade to reach
the lower standard-deviation boundary, as compared to its corresponding upper
standard-deviation boundary.)
However, for the standard deviation calculation to be statistically reliable, it
needs at least 20 to 30 observations (close-to-close moves), which means the look-
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back period for the calculation will be a little longer than desirable for a short-term
system. Remember, we strive to find a maximum trade length of no more than 10
days, because that’s how long the market will remember why it took off one way
or another, and created our trading opportunity in the first place. By the same
token, we shouldn’t use any more data than that to calculate our stops and exit
points when entering the trade. If we use more data than necessary, that data will
be obsolete and only help us arrive at a suboptimal solution. If it’s reasonable to
believe that the market will only remember what triggered a trade for five to ten
days, then it’s equally reasonable to assume that the market won’t remember the
fundamental reasons leading into the trade for more than five to ten days either.
The second way to measure volatility is the average true range method,
which is very well known in technical analysis circles. To calculate the daily true
range, simply take the highest of the previous day’s close and today’s high, and
subtract the lowest of the previous day’s close and today’s low. Most often the daily
true range simply will be the distance between today’s high and low, but on days
when the market gaps higher or lower, that gap will be accounted for by adding the
distance between yesterday’s close and whichever of today’s extremes is closest to
it. To calculate the average true range over a certain number of bars or days, simply sum up all true ranges for all bars in the lookback period and divide by the
number of bars.
The calmer the market over the lookback period, the smaller the average true
range and the closer the stops and exits will be to the entry price. For example, if
the average true range over the lookback period is 4 percent, and you’ve decided
to place a stop two average true ranges away from the entry price, then that stop
will be 8 percent away. If the price of the stock is $100, the stop will be placed $8
away, but if the price of the stock is $50, then the stop will be $4 away from the
entry price. If, on the other hand, the average true range was only 3 percent, then
a stop loss will be placed $6 away from a $100 stock and $3 away from a $50
stock. In this way, the average true range becomes a universal measure that can be
applied to all stocks, no matter the price.
The major advantage of the average true range method, compared to the standard deviation method, is that the former doesn’t need as much data to make the
calculations reliable.
The major disadvantage of the average true range method, compared to the
percentage method, is that the former needs a certain amount of historical data for
its calculations, which presents yet another optimization problem. To solve this, I
have equalized the lookback period for the average true range calculation with the
maximum allowed holding period for a trade. For example, if the maximum holding period for a trade is set to six days, then the lookback period for the average
true range calculation also will be six days. Likewise, if I test a system using varying holding periods, say from one to ten days, in steps of one day, the lookback
period for the average true range calculation will always be the same as the max-
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imum holding period. This makes perfect sense in regard to the memory of the
market. We’ll take a close look at this second volatility method shortly, but first
we need to learn how to analyze the results.
SURFACE CHARTS
When trying to figure out where to place the stops in the system I’m working with,
I like to use a surface chart, which provides an excellent method for getting a feel
for how the output variable (for example, the average profit per trade) reacts to two
different input variables (for example, the stop-loss and profit-target distances)
and how the inputs are interacting with each other. In the upcoming analysis of our
systems, we look at the following output variables and how they change with the
addition and changes to the various stops we already have defined:
■
■
■
The average profit per trade
The standard deviation of all trades
The average percentage of winning trades
Of course, one can use other evaluation parameters and output variables as
well, such as the final net profit, drawdown, profit factor (gross profit divided by
gross loss), average trade lengths, and the average number of trades. But at some
point it becomes information overload, and we won’t be able to digest it all—not to
mention the redundancy of the output variables basically telling us the same thing.
Figures 19.1 and 19.2 show what a couple of typical surface charts look like.
In Figure 19.1, the output variable is the average profit per trade. In Figure 19.2,
the output variable is the risk–reward ratio (the average profit per trade, divided by
the standard deviation of all trades). The different values of the output variable are
represented by the different colors. The legend to the right of the chart tells us
which specific value each color represents. The values for the input variables are
represented by the numbers on the horizontal and vertical axes. The output variables for both figures are the maximum allowed trade length on the horizontal
axis, and the stop loss on the vertical axis. The numbers on the axis tell us that this
particular system has been tested for maximum trade lengths varying from one to
ten days, in steps of one day, and for stop-loss distances away from the entry price
varying from 0.2 percent to 2 percent, in increments of 0.2 percent.
The grid inside the charts helps us find the output value that corresponds to
a specific combination of the input variables. For example, in Figure 19.1, the little square surrounds the intersection on the grid that represents a system with a
four-day maximum allowed trade length and a 1 percent stop loss. Matching the
color that covers this area of the chart with the colors in the legend, we see that this
version of the system produced an average profit per trade somewhere between 0.4
and 0.5 percent. To be prudent, we will go with the lower value and say that the
average profit per trade is 0.4 percent.
CHAPTER 19
FIGURE
Placing Stops
213
19.1
Surface chart with average profit per trade as output variable.
When reading surface charts, look for as many large, preferably uninterrupted,
areas of the same color as possible, which represent values as high as possible, as
indicated by the legend. In this way, we’ll make sure that the system not only works
with that specific variable combination but also with other adjacent combinations,
which gives us some room for error and adjustments if market conditions change.
If you look at the color chart as a weather map, with each line separating the
different colors representing the air pressure lines on the weather map, the tighter
the lines, the more unstable the weather, with really tight lines forming a tornado
or hurricane (or at least a very unstable weather situation) that no one wants to be
in. Or look at the chart as a topographical map, with the colors representing
changes in elevation. With that in mind, it is easy to understand that you’d be standing safer on a large, relatively flat and uninterrupted plateau than on a pointy peak.
Also, when putting together charts like this, it’s important to have a feel for
what will likely be the best values for the input variables, given the desired char-
214
FIGURE
19.2
Surface chart with risk–reward ratio as output variable.
acteristics of the system, so that the very best values don’t fall on the very edge of
the chart. If they do, there is no way of knowing how the system will perform if
the conditions happen to change in the wrong direction and cause the best variable
combinations to fall outside of the chart.
The larger square in Figure 19.1 encapsulates an area that is relatively large
and flat, which suggests that all trade-length/stop-loss combinations surrounding
the four-day/1-percent combination in the little square will produce similar results.
Therefore, the best alternative in this chart is the four-day/1-percent combination,
and if it just so happens that adjacent combination would have worked better in
real-life trading, at least we’ve gotten close enough to that combination to make a
profit, or at least avoid a catastrophe.
However, just looking at one chart like this isn’t enough; and that is where
Figure 19.2 comes into play. Figure 19.2 shows the risk–reward ratio as the average profit per trade, divided by the standard deviation of all trades. The greater the
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risk–reward ratio, the greater the profit in relation to the uncertainty of the outcome, and the better off we are. In the case of the four-day/1-percent combination
from Figure 19.1, the risk–reward ratio comes out to 0.6. According to Figure 19.2,
this is as good as it will get, given the information from this chart.
To put together a surface chart in Excel, the data first need to be organized
in a matrix, like the portion of one shown in Figure 19.3, which depicts the data
behind the chart in Figure 19.1. Looking at the numbers in Figure 19.1, we can see
that the four-day/1-percent combination in fact has an average profit of 0.450 percent per trade, but also that this wasn’t the highest value. In fact, a couple of values in the one-day column are much higher, but because they also are surrounded
by lower values, they do not represent as robust and stable variable combinations
as the four-day/1-percent combination. With the data organized in this way, all you
have to do is click the chart wizard button in Excel and follow the instructions. To
get the data collected into a matrix is, however, a completely different story. The
data are normally organized into columns, as in Figure 19.4, which show a small
part of the data behind the matrix in Figure 19.3.
The data sort, row( ), column( ), and index( ) functions in Excel are used to
move data from the columns in Figure 19.4 to the matrix in Figure 19.3.
Getting the data into the columns in Figure 19.4 is a whole lot easier, but let’s
examine the columnar data. In this case, column A holds the ticker symbol for the
markets tested; column B holds an index number for the test run (we will talk more
about this later); column C holds the values for the stop-loss input variable; column
D holds the values for the trade-length input variable: and column E holds the values for the output variable, which in this case is the average profit per trade.
Note that in the case of Figure 19.4, each market has been tested 10 times
with the exact same setting for the input variables (columns C and D), but with a
FIGURE
19.3
Matrix of data for Excel chart.
216
FIGURE
19.4
Columnar arrangement of data for surface chart.
different value for the output variable for each test run (column E). How can that
be? This is because these data are used to develop the system using a random-entry
method that allowed us to test all the individual signals the system generated,
regardless of whether all signals would have been traded, depending on if we
would have been in a trade or not already. The numbers in column B keep track of
each test run. For each test run, each time the system encounters a bar in a market
with all its regular entry criteria fulfilled, the system will enter the trade at random.
In some test runs it will, in others it won’t. Thus, although many of the trades will
be the same in many of the test runs, each test run will hold a completely unique
set of trades, different from all other test runs, which then results in a different
average profit per trade.
For the purposes of this book, I did not use the random-testing procedure
because it adds to the time it takes to test a system. I will, however, incorporate the
possibility for you to do so yourself, in the code I present in an upcoming chapter.
Be warned, though, this can be a very time-consuming task.
It also is very difficult to test more than three variables at one time, and you
can only examine the variables two at the time. Consider the testing we will walk
through: I will test ten values each for three variables at the time for two different
exit and stop concepts. For each test run, only one variable will alter its value,
while the other variables remain constant. Thus, each test will have to run through
each stock 2,000 times (10 * 10 * 10 * 2). Had I added the random-entry feature
and asked the system to test each stock an additional 10 times, each stock would
have been tested a total of 20,000 times. With the computer I’m using, a dual
processor 500 MHz Pentium III, with 256 MB RAM, running one system through
CHAPTER 19
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217
one stock takes about 40 minutes. Running one system through all 65 stocks takes
about 45 hours. And I had to do 10 tests like this. I dare to say that no one has ever
done such a thorough back testing of their systems before they try to sell them to
you for prices many times higher than the price of this book.
Also, even if I wanted to test each stock 20,000 times or more, I wouldn’t be
able to do so in a convenient manner with this many stocks. Excel can only hold a
little more than 65,000 rows of data, and with 65 stocks tested at 1,000 times each
per exit concept, that’s exactly how many rows of data each Excel file will hold.
We have simply reached the ceiling for what today’s computers and software packages allow us to do.
Before we move on, I also would like to point out that you could use this type
of testing procedure to test your entry rules as well. This works especially well if
you use indicators and patterns that can vary in length and lookback periods, such
as moving averages and crosses above and below the highs and the lows over a certain number of days.
CHAPTER
20
Adding Exits
I
n Part 2, it became obvious that most systems didn’t work all that well when traded from the short side, so from now on we will place most of our focus on the long
side. However, when testing the stops, we will test both sides simultaneously and
use the settings that work the best, on average, on the long side only. The reason
for this is basically the same as for why we want to test a system in as many markets as possible, and why we want every market, profitable or not, to influence the
final parameter settings to an equal degree. Namely, we never know when a profitable market will start behaving as a unprofitable market (and vice versa).
Therefore, we want to prepare ourselves by letting the unprofitable markets influence the variable settings so that when less-profitable periods come along, at least
they won’t ruin us completely.
The same reasoning goes for the long and short trades. We never know when
the now-profitable long side will start to behave as the less-profitable short side.
Therefore, we want to prepare for that by letting the short side influence the variable settings from the very beginning. This will lower the profit potential for all
long trades, but also make it more likely that a bad period will only end in a modest drawdown instead of a complete disaster.
Yet another reason for not testing the long and the short sides separately from
each other is a more pragmatic one. Namely, it will double the number of test runs
necessary, to 4,000 runs per stock, or as many as 40,000 runs per stock, had I
included the random-testing procedure as well.
For each system, four stops and exit versions will be examined. Two versions
will be based on a regular percentage-stop method, and two versions will be based
on the true-range method. One version from each of these two methods will work
219
220
with a stop loss, profit target, and time-based stop, while the other version will
work with a trailing stop, profit target, and time-based stop.
Let’s start the testing procedure using the code given in the next section on
the first of our systems, Hybrid system No. 1, featured in the September 2000
issue of Active Trader magazine. With four stops and exit versions per system,
comparing all input variables with each other two at a time, looking at three different output variables, this research will produce a hell of a lot of surface charts.
Because of the large number of charts produced for each system, I will describe
the complete process only for one of the two most profitable versions of the first
system. For other versions and systems, I will only briefly comment on the result
and illustrate it with a chart or two and a few summary tables.
The research is only performed on the five short-term systems that don’t
depend on any intermarket relationships. These five systems are Hybrid system
No. 1; Meander system, V.1.0; volume-weighted average; Harris 3L-R pattern
variation; and expert exits. The other three systems, RS system No. 1, Relative
strength bands, and Rotation, will be filter-tested later.
SURFACE CHART CODE
{Export for finding optimal stops with surface charts in Excel.
{1} Set SurfaceChartTest(True)}
Variable: SurfaceChartTest(True);
If SurfaceChartTest = True Then Begin
{2} Inputs:
TestRunVar(1), StopTypeVar(1), StopLossVar(1), ProfTargVar(4.5),
TrailStopVar(0), MaxBarsVar(8);
Variables:
SCT.LongLoss(0), SCT.ShortLoss(0), SCT.LongTrailing(0),
SCT.ShortTrailing(0), SCT.LongTarget(0), SCT.ShortTarget(0),
SCT.TrueLength(0), EP(0), SCT.TRLoss(0), SCT.TRTarget(0),
SCT.TRTrailing(0);
{Code for stop type 1 (percentage stops) goes here, see below. Set
StopTypeVar(1)}
{Code for stop type 2 (true-range stops) goes here, see below. Set
StopTypeVar(2)}
Variables:
SCT.TradeType(""), SCT.NameLength(0), SCT.StopType(""),
AvgTradeVar(0), StDevVar(0), NoTradesVar(0), PercWinVar(0),
SCT.MarketPos(0), SCT.PosProfit(0), SCT.SetArrayPos(0),
SCT.SumProfit(0),
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221
SCT.ArrayPosition(0), SCT.WinTrades(0), SCT.SumSqProfit(0),
SCT.TestString(""), SCT.FileString("");
{3} Arrays:
SCT.TradeProfit[2000](0);
If AllowLong = True Then
SCT.TradeType = "Long";
If AllowShort = True Then
SCT.TradeType = "Short";
If AllowLong = True and AllowShort = True Then
SCT.TradeType = "Both";
SCT.NameLength = StrLen(GetStrategyName) - 6;
If StopTypeVar = 1 Then
SCT.StopType = "Perc-"
Else If StopTypeVar = 2 Then
SCT.StopType = "TR-";
SCT.FileString = "D:\BookFiles\" + SCT.StopType + "Test - " +
RightStr(GetStrategyName, SCT.NameLength) + " - " +
RightStr(NumToStr(CurrentDate, 0), 4) + ".csv";
{SCT.TestString = "Market" + "," + "Direction" + "," + "Test Run" + "," +
"Stop Loss" + "," + "P-Target" + "," + "Trail Stop" + "," + "Max Bars" +
"," + "Avg Trade" + "," + "StDev Prof" + "," + "No Trades" + "," + "Perc
Win" + NewLine;
FileAppend(SCT.FileString, SCT.TestString);}
End;
{5} NoTradesVar = TotalTrades;
SCT.MarketPos = MarketPosition;
If NoTradesVar > NoTradesVar[1] Then Begin
If MarketPosition(1) = 1 Then
SCT.PosProfit = (ExitPrice(1) - EntryPrice(1)) / EntryPrice(1);
If MarketPosition(1) = -1 Then
SCT.PosProfit = (EntryPrice(1) - ExitPrice(1)) / EntryPrice(1);
SCT.TradeProfit[SCT.SetArrayPos] = SCT.PosProfit;
SCT.SetArrayPos = SCT.SetArrayPos + 1;
End;
{6} If LastBarOnChart Then Begin
{Alt: If LastCalcDate = Date + 1 Then Begin}
222
For SCT.ArrayPosition = 0 To (NoTradesVar - 1) Begin
SCT.SumProfit = SCT.SumProfit +
SCT.TradeProfit[SCT.ArrayPosition];
If SCT.TradeProfit[SCT.ArrayPosition] > 0 Then
SCT.WinTrades = SCT.WinTrades + 1;
{7} End;
If NoTradesVar <> 0 Then Begin
AvgTradeVar = SCT.SumProfit / NoTradesVar;
PercWinVar = SCT.WinTrades * 100 / NoTradesVar;
End
Else Begin
AvgTradeVar = 0;
PercWinVar = 0;
End;
{8} For SCT.ArrayPosition = 0 To (NoTradesVar - 1) Begin
SCT.SumSqProfit = SCT.SumSqProfit +
Square(SCT.TradeProfit[SCT.ArrayPosition]);
{9} End;
If NoTradesVar <> 0 Then
StDevVar = SquareRoot((NoTradesVar *
SCT.SumSqProfit - Square(SCT.SumProfit)) / (NoTradesVar *
(NoTradesVar - 1)))
Else
StDevVar = 0;
{10}
SCT.TestString = LeftStr(GetSymbolName, 5) + "," + SCT.TradeType
+ "," + NumToStr(TestRunVar, 0) + "," + NumToStr(StopLossVar, 2) + ","
+ NumToStr(ProfTargVar, 2) + "," + NumToStr(TrailStopVar, 2) + "," +
NumToStr(MaxBarsVar, 0) + "," + NumToStr(AvgTradeVar * 100, 2) +
"," + NumToStr(StDevVar * 100, 2) + "," + NumToStr(NoTradesVar, 0) +
"," + NumToStr(PercWinVar, 2) + "," + NewLine;
FileAppend(SCT.FileString, SCT.TestString);
End;
End;
{11} Code for stop type 1 (percentage stops).}
If StopTypeVar = 1 Then Begin
SCT.LongLoss = 1 - StopLossVar * 0.01;
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223
SCT.ShortLoss = 1 + StopLossVar * 0.01;
SCT.LongTrailing = 1 - TrailStopVar * 0.01;
SCT.ShortTrailing = 1 + TrailStopVar * 0.01;
SCT.LongTarget = 1 + ProfTargVar * 0.01;
SCT.ShortTarget = 1 - ProfTargVar * 0.01;
End;
If MaxBarsVar > 0 and BarsSinceEntry + 1 >= MaxBarsVar Then
SetExitOnClose;
If StopLossVar > 0 Then Begin
ExitLong ("SCT.L-Loss(P)") Next Bar at EntryPrice * SCT.LongLoss
Stop;
ExitShort ("SCT.S-Loss(P)") Next Bar at EntryPrice * SCT.ShortLoss
Stop;
End;
If TrailStopVar > 0 Then Begin
SCT.TrueLength = BarsSinceEntry + 1;
ExitLong ("SCT.L-Trail(P)") Next Bar at
Highest(High, SCT.TrueLength) * SCT.LongTrailing Stop;
ExitShort ("SCT.S-Trail(P)") Next Bar at
Lowest(Low, SCT.TrueLength) * SCT.ShortTrailing Stop;
End;
If ProfTargVar > 0 Then Begin
ExitLong ("SCT.L-Trgt(P)") Next Bar at EntryPrice * SCT.LongTarget
Limit;
ExitShort ("SCT.S-Trgt(P)") Next Bar at EntryPrice * SCT.ShortTarget
Limit;
End;
End;
End
{12} Code for stop type 2 (true-range stops).}
Else If StopTypeVar = 2 Then Begin
EP = EntryPrice;
If TrailStopVar <= 0 and EP <> EP[1] and EP > 0 Then Begin
SCT.TRLoss = AvgTrueRange(MaxBarsVar) * StopLossVar;
SCT.TRTrailing = AvgTrueRange(MaxBarsVar) * TrailStopVar;
SCT.TRTarget = AvgTrueRange(MaxBarsVar) * ProfTargVar;
224
End
Else If TrailStopVar > 0 Then Begin
SCT.TRLoss = AvgTrueRange(MaxBarsVar) * StopLossVar;
SCT.TRTrailing = AvgTrueRange(MaxBarsVar) * TrailStopVar;
SCT.TRTarget = AvgTrueRange(MaxBarsVar) * ProfTargVar;
End;
If MaxBarsVar > 0 and BarsSinceEntry + 1 >= MaxBarsVar Then
SetExitOnClose;
If StopLossVar > 0 Then Begin
ExitLong ("SCT.L-Loss(TR)") Next Bar at EntryPrice - SCT.TRLoss
Stop;
ExitShort ("SCT.S-Loss(TR)") Next Bar at EntryPrice + SCT.TRLoss
Stop;
End;
If TrailStopVar > 0 Then Begin
SCT.TrueLength = BarsSinceEntry + 1;
ExitLong ("SCT.L-Trail(TR)") Next Bar at
Highest(High, SCT.TrueLength) - SCT.TRTrailing Stop;
ExitShort ("SCT.S-Trail(TR)") Next Bar at
Lowest(Low, SCT.TrueLength) + SCT.TRTrailing Stop;
End;
If ProfTargVar > 0 Then Begin
ExitLong ("SCT.L-Trgt(TR)") Next Bar at EntryPrice + SCT.TRTarget
Limit;
ExitShort ("SCT.S-Trgt(TR)") Next Bar at EntryPrice - SCT.TRTarget
Limit;
End;
End;
End;
1.
The variable SurfaceChartTest(True) needs to be placed on top of the code
or even as an input. The other variables will only become active when
SurfaceChartTest is set to True. To speed up the computing time, the program
will not run through the rest of the code, as long as SurfaceChartTest is set
to False.
CHAPTER 20
Adding Exits
2.
225
The input TestRunVar will not be used here, but is present so that you can
run through your own systems using the random-entry feature. The code for
the random-entry feature can look something like this:
Variable: RandomTrigger(0);
RandomTrigger = IntPortion(Random(2));
If RandomTrigger = 1 and (rest of entry criteria) Then Begin
Final buy or sell trigger rule
An example of how to use the code can be found in Part 2.
We need to create one array to contain the data for our calculations. We could
have done without the array and instead run through all the calculations for
each bar, but to speed up the computing time, we will do most of the calculations only once, on the very last bar on the chart. The array is now set to
hold 2,000 trades. The larger the arrays, the slower the calculations, so you
might want to change this number to what makes the most sense for the system you currently are working on.
4. These calculations and exports only need to be done once, on the very first
bar on the chart. By altering the state of the variables AllowLong and
AllowShort at the very top of the code (see the code for any of the individual systems), we can test all long and short trades, either separately from
each other or together. Then we create the file that we will import into Excel
(variable SCT.FileString) and the column headers for the data we need to
export later (variable SCT.TestString).
5. These calculations are done on every bar on the chart. We are now filling the
array SCT.TradeProfit with the end result of each trade. An array is a series
of values stored in a specific order. In this case, the first position in the array
will hold the result of the first trade, and so on.
6. All remaining calculations will only be executed on the very last bar of the
chart. Note: If you plan to use this code and use the criteria Open Next Bar
(or Open Tomorrow) for your entries and exits, you must use the alternative
function. First, we run a loop (that starts with the word “For”) to calculate the
total profit (variable SCT.SumProfit) by adding all the values contained in
the array SCT.TradeProfit. We also count the number of winning trades in
the variable SCT.WinTrades.
7. Moving out of the first loop, we now calculate the variables AvgTradeVar and
PercWinVar, which are self-explanatory.
8. The second loop (also starting with the word “For”) sums up the squared
profits from all trades in the SCT.SumSqProfit variable.
9. Moving out of the second loop, we calculate the standard deviation of all
trades (variable StDevVar).
10. Finally, all the necessary data will be stored in the variable SCT.TestString
and exported into a file that we can open with Excel, with the help of the
3.
226
SCT.FileString. The file export takes place in the command FileAppend. The
name of the file is specified by the variable SCT.FileString, created in step 4.
11. The code for the stop type 1 (the percentage stop) will test the following four
exit techniques: the stop loss, the profit target, the trailing stop, and the timebased stop. In the first round of testing, we will leave out the trailing stop. In
the second run of testing, we will leave out the stop loss, letting the trailing
stop function as a stop loss as well.
12. The code for the stop type 2 (the true-range stop) will test the following four
exit techniques: the stop loss, the profit target, the trailing stop, and the timebased stop. In the first round of testing, we will leave out the trailing stop. In
the second run of testing, we will leave out the stop loss, letting the trailing
stop function as a stop loss as well. When testing using the stop loss, the true
ranges used will be fixed at the day for the entry. When testing with the trailing stop, the true ranges will be recalculated for each bar. In both cases, the
lookback period for the average true ranges is set to equal the maximum
allowed trade length as defined by the variable MaxBarsVar.
HYBRID SYSTEM NO. 1
In the case of the Hybrid system, it turned out that the true range-based stops produced the best results. Remember, we tested two different concepts of each stop
and exit methodology, and two different methods of each concept.
Stop-loss Version
For the true range concept, method one consisted of a stop loss (varying between
0.2 and 2 average true ranges, in steps of 0.2), a profit target (varying between 0.5
and 5 average true ranges, in steps of 0.5), and a maximum trade length (varying
between 1 and 10 bars, in steps of 1).
The best way to sift through all the surface charts produced by the code, is to
start by looking at the standard deviations of the returns, which should be as low
as possible. This will give us a first clue on how to interpret the rest of the data.
Figures 20.1 to 20.3 show the standard deviations of the returns for various combinations of the input variables. In Figure 20.1, for example, the input variables are
the profit target on the x-axis and the stop loss on the y-axis.
To keep the standard deviations as low as possible, Figures 20.1 to 20.3 indicate that we should strive to come up with a combination of the three input variables that place us as far down and as far to the left as possible in all the other
charts. This means that the values for all input variables should be as low as possible. (This will hold true for all other systems as well.)
Figure 20.4 shows the average profit per trade in relation to the profit target and
the stop loss. As you can see, a profit target between 1 and 1.5 average true ranges
FIGURE
20.1
Standard deviation of returns (1).
FIGURE
20.2
227
FIGURE
20.3
FIGURE
20.4
Average profit per trade versus profit target and stop loss.
228
CHAPTER 20
Adding Exits
229
(ATR) will produce the highest average profit per trade (as indicated by the legend to
the right of the chart), together with any stop loss ranging from 0.8 to 2 ATR.
However, because of the information from Figure 20.1, we know that the tighter the
stop loss the better off we will be when it comes to the system’s risk–reward ratio.
Figure 20.5 shows the average profit per trade in relation to the maximum
trade length and the profit target. In this case, it is easy to see that the best choice
for the maximum trade length is six days, which works with almost all profit target distances. At this point, we can decide that the maximum trade length should
be six days and the profit target should be placed either 1 or 1.5 ATRs away from
the entry price. All that is left is to see if we can fit a stop loss into the mix that
preferably should be no larger than 1.2 ATRs.
Figure 20.6 confirms that the maximum trade length should be six days. From
Figure 20.6 we can see that the best choice for our stop loss is to place it 1 ATR
from the entry price, because this stop loss is the tightest stop that is surrounded by
two other stops that produce similar results. The 0.8 ATR stop is not a good alternative, because of the lower average profit produced by the 0.6 ATR stop.
FIGURE
20.5
Average profit per trade versus maximum trade length and profit target.
230
FIGURE
20.6
Maximum trade length of six days.
Now we’ve decided that the stop loss should be placed 1 ATR away from the
entry price and that the maximum trade length should be six days. It remains to be
seen whether the profit target should be at 1 or 1.5 ATRs. In this case, I decided to
place it at 1.5 ATRs, which is slightly contradictory to what we learned from
Figures 20.1 to 20.3. However, had I placed the stop at 1 ATR, the risk–reward
relationship going into any individual trade would have been 1:1. Going with a
higher profit target for an initial risk–reward relationship of 1.5:1 (or 3:2) will
demand a lower percentage of profitable trades.
This makes sense when looking at Figures 20.7 to 20.9, all of which suggest
that the number of profitable trades will fall somewhere in the 40 to 50 percent
region. Note, however, that these results were derived from testing both sides of
the market (both long and short trades). But because we already know from Part
2 that the short side most likely won’t perform as well, the results for the long
side most likely will be better than indicated by these charts. Hopefully, the
results also will be better than where we left off in Part 2 (at this point I honestly don’t know).
FIGURE
20.7
Number of profitable trades, variable 1.
FIGURE
20.8
231
232
FIGURE
20.9
Plugging these stops with the values suggested by the surface charts into the
system as we left it in Chapter 8, and then testing it on long trades only, produced the
results in Table 20.1. Comparing this table with Table 8.4, we can see that using the
stops and exits from our research made quite an improvement, despite a much lower
average profit per trade and lower profit and risk factors. Improvement number one
is a much higher risk–reward ratio of 1.26, which means that the individual trades
have become more homogenous and similar to each other, which in turn means that
the risk is much lower. This is also reflected in much lower standard deviations for the
profit and risk factors. The second improvement is a much higher percentage of profitable trades, which, if nothing else, should make the system more fun to trade. The
drawdown measured in percentage terms also is a little lower than in Table 8.4.
Last but not least, the average trade length has decreased by more than 60
percent, which also has resulted in much less time spent in the market. At the same
time, the average profit per trade is only cut in half. Thus, the trades we make with
the optimized stops and exits are much more profitable and efficient per days
spent in a trade. Theoretically speaking, spending only one-third of the time in a
CHAPTER 20
Adding Exits
233
TAB LE
20.1
Results of Stop-loss Version for Hybrid System
Long only: 1 ATR stop loss,
1.5 ATR profit target, 6 bars max. trade length
PercProf: 92.31
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
261.09
56.83
50.27
3.41
109,684.19
78,567.54
452.49
358.72
4,724.28
Market
0.10
High:
Low:
317.92
204.26
53.68
46.87
188,251.72
31,116.65
811.21
93.77
5,176.77
(4,271.79)
Portfolio
1.26
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.29
0.23
1.52
1.06
0.14
0.10
0.24
0.04
57,809.84
32,859.60
90,669.44
24,950.25
30.26
18.62
48.88
11.64
31.18
3.84
35.02
27.33
4.94
0.26
5.20
4.68
Average:
St. Dev:
High:
Low:
trade per market means that we could stay fully invested all the time by jumping
from trade to trade among three markets. In that case, the net profit from trading
all three markets would be three times the average net profit in Table 20.1, which
would be far greater than the average profit from Table 8.4.
Also note that the average trade length in Table 20.1 is close to five days.
However, as opposed to the maximum trade length behind the surface charts, this
number includes weekends and holidays, which means that the effective trade
length, measured in number of bars, is slightly shorter. The average trade length
also counts the entry and exit bars as full trading days, which means that another
full trading day (or bar) can be deducted from that number.
The number of bars spent in a trade also relates to the average percentage of
profit per trade of around 0.2 percent per trade, as indicated by the surface charts.
Now, 0.2 percent per trade for a trade lasting on average around three days (or around
0.07 percent per day) doesn’t sound like much. But we have to remember that this is
on the average for all trades: Both the average winning and average losing trades
are larger than this. And if we do the math, 0.07 percent per day for a full year isn’t
bad at all, as it actually comes out to a simple (noncompounded) yearly return of 17.5
percent (0.07 * 250 trading days), or a compounded return of 19 percent
(1.0007^250), which is well above the long-term buy-and-hold average of 12 percent.
Trailing-stop Version
Staying with the true-range concept but substituting the stop-loss method with a
trailing stop method produced another profitable stop and exit combination for
234
this system. First, let’s take a look at Figures 20.10 to 20.12, which show the average profit per trade in relation to the three input variables. It is evident that the
maximum trade length should be six days. What is not so obvious, however, is
what the values for the profit target and trailing stop should be. In situations like
this, there is room for some personal interpretations and compromises that make
the most sense to you as an analyst.
Looking at Figure 20.11, the 3-ATR profit target seems to be the best profit
target to go with a six-day maximum trade length, because it is the lowest value
surrounded by equally good values above and below it. The same reasoning
applies to Figure 20.12, which suggests the trailing stop should be placed 1.5 ATR
away from the highest high price during the life of the trade. However, combining
these findings and the data from Figure 20.10 places us on the slope of a not-soprofitable area (remember the analogy to the topographical map, in Chapter 19)
with plenty of other low-profit variable combinations surrounding it. It is better to
lower the trailing stop to 1.2 ATR, so that we at least end up on top of the most
profitable zone.
FIGURE
20.10
Average profit per trade for input variable 1.
FIGURE
20.11
FIGURE
20.12
235
236
But even so, Figure 20.10 shows this is not as good a solution as, for example, a 2.4 ATR trailing stop combined with a 1 ATR profit target. The main disadvantage with the latter combination is, however, that it takes us too far to the right
in the chart, which increases the standard deviation of the profits. A 1 ATR profit
target also doesn’t match as well as a 1.2 ATR trailing stop with what we learned
to be the best solution in Figure 20.11. Lastly, it also gives us a weird risk–reward
relationship going into any individual trade. Therefore, and despite the disadvantages of a 3 ATR profit target and 1.2 ATR trailing stop, it seems to be the best
combination together with the six-day maximum trade length. Sometimes you just
have to make a few compromises.
Table 20.2 shows the result for this version of the system when tested on
our 65 markets. Compared to the version featured in Table 20.1, this version
seems to be a little more profitable, as indicated by the higher profit and risk
factors, but also a little riskier, as indicated by the higher standard deviations for
the same. However, the only reason why this version of the system seems to be
a little more profitable is that it trades a little more often, with 278 trades on
average per market. Strangely, this happens despite a slightly longer average
trade length, which illustrates the fact that there are no sure conclusions to be
made when changing the rules for the system, however small these changes
might be. Note also that because the average profit per trade is almost
unchanged, this version of the system is not as efficient per bars or days in trade
as that in Table 20.1. Nonetheless, we will continue to work with both to see how
they fare in the competition.
TAB LE
20.2
Results of Trailing Stop on Hybrid System
Long only: 1.2 ATR trailing stop,
3 ATR profit target, 6 bars max. trade length
PercProf: 93.85
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
278.25
62.58
43.94
4.43
119,238.87
82,037.26
456.56
345.76
4,877.49
Market
0.10
High:
Low:
340.82
215.67
48.37
39.51
201,276.13
37,201.61
802.32
110.80
5,334.05
(4,420.93)
Portfolio
1.32
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.35
0.38
0.18
0.16
65,289.25
39,924.48
31.68
18.60
34.21
4.31
5.09
0.23
High:
Low:
1.73
0.97
0.35
0.02
105,213.73
25,364.77
50.28
13.08
38.52
29.91
5.32
4.87
CHAPTER 20
Adding Exits
237
MEANDER SYSTEM, V.1.0
The meander system also did best with stops and exits based on the true-range
concept. The first of the two versions operates with a stop loss of 1.8 ATR, a profit target of 3 ATR, and a maximum trade length of nine days. Figures 20.13 to
20.15 illustrate how these numbers where derived.
Stop-loss Version
From Figure 20.13 we can see that to get as many profitable trades as possible, the
profit target should be as close to the entry as possible. But even with a profit target as far away from the entry as 4.5 ATR, the number of profitable trades still
exceeds 50 percent, as long as the stop loss is sufficiently far away from the entry
as well. However, what is alarming in Figure 20.13, which also finds confirmation
in Figure 20.14, is that the stop loss probably needs to be further away from the
entry than the 2 ATR that we’ve decided to be the maximum. We really should re-
FIGURE
20.13
Profit target versus number of profitable trades.
FIGURE
20.14
A stop loss of 1.8 ATR.
FIGURE
20.15
Maximum trade length versus number of profitable trades.
238
CHAPTER 20
Adding Exits
239
run the optimization procedure and allow for even larger stop-loss distances, but
for the purposes of this book, these results will have to do.
Moving on, Figure 20.14 tells us we have no other choice than to go with a
1.8 ATR stop loss (never go with the extreme values of the charts, because we have
no idea of what’s happening with values outside it), combined with a maximum
trade length of eight or nine days. By doing so, the legend in Figure 20.14 indicates that the average profit per trade will be at least as high as 0.48 percent per
trade, regardless of the number of ATRs we choose for the profit target. The major
disadvantage with this setting is, however, that it is in the upper right-hand corner
of the chart, which means the standard deviation (and thereby the risk) will be high
as well. (To get the best risk–reward relationship, try to keep the input variables as
short-term as possible.)
Comparing our findings in Figure 20.14 with the information in Figure
20.15, we can see that we probably are better off with a maximum trade length of
eight days. Not only will that take us a little further to the left of the chart, but
given that the estimated profits are pretty much the same for the eight- and nineday settings, an eight-day setting will give us a little more bang for the buck in
regard to trading efficiency. Figure 20.15 also indicates that we should go with a
profit target of 3 ATR away from the entry price.
Table 20.3 shows the results of plugging these values into the meander system, substituting the original stops and exits, and then testing the system on the
same markets as before. Before we compare Table 20.3 with Table 10.5, again note
that the average trade lengths in Table 20.3 are longer than the maximum trade
lengths specified by the exit rules. This is because the average trade lengths in the
TAB LE
20.3
Results of Stop Loss for Meander System
Long only: 1.8 ATR stop loss,
PercProf: 90.77
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
198.42
48.26
53.83
4.70
149,951.03
94,746.93
838.77
621.34
6,484.33
Market
0.12
High:
Low:
246.67
150.16
58.54
49.13
244,697.96
55,204.10
1,460.11
217.43
7,323.11
(5,645.56)
Portfolio
1.35
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.39
0.27
0.17
0.11
65,254.96
36,474.46
30.82
19.36
39.76
6.06
8.32
0.40
High:
Low:
1.66
1.11
0.28
0.06
101,729.42
28,780.50
50.18
11.46
45.82
33.70
8.71
7.92
240
tables also count the weekends and holidays. You can get a better estimate for the
effective average trade length by using the following formula:
EAL TAL * (250 / 365) 1
Where:
EAL Estimated average trade length
TAL Table average trade length
This gives an effective estimated average trade length of 4.70 days (8.32 *
250 / 365 1) for the version of the meander system featured in Table 20.3. You
can apply the same formula on all systems to come.
Comparing Table 20.3 with Table 10.5, the first thing to notice is that we
actually managed to increase the average profits per trade, from $788 in Table 10.5
to $839 in Table 20.3. Not only did the average profit per trade increase, we also
managed to do so while increasing the risk–reward ratio from an already very high
1.21 to 1.35. Additional good news is that the standard deviations for both the
profit and risk factors decreased as well.
Table 20.4 shows the results from another version of this system, made up of a
trailing stop of 2.7 ATR, a profit target of 3.5 ATR, and a maximum trade length
of nine days. Because the surface charts showed little of interest, I left them out of
the analysis for this version of the system.
TAB LE
20.4
Results of Trailing Stop for Meander System
PercProf: 93.85
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
188.14
45.16
52.67
4.16
156,028.96
98,506.56
916.86
674.05
6,968.87
Market
0.13
High:
Low:
233.30
142.98
56.83
48.51
254,535.52
57,522.40
1,590.91
242.81
7,885.73
(6,052.01)
Portfolio
1.36
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.40
0.28
0.18
0.12
65,561.77
37,024.95
31.53
17.47
43.65
6.53
9.62
0.45
High:
Low:
1.68
1.12
0.30
0.07
102,586.72
28,536.82
49.00
14.07
50.18
37.12
10.07
9.17
CHAPTER 20
Adding Exits
241
The reasoning used in the stop-loss version of the system also holds true for
the trailing-stop version, with the addition that the trailing-stop version even is a
tad better still.
All in all, we can be very sure that we will be able to repeat these historical
and hypothetical results in the future when we trade meander on previously unseen
data. The only two negatives are the amount of time spent in the market and the
percentage drawdowns, which still are relatively high compared to the version
depicted by Table 10.5. Nonetheless, we’re looking forward to continuing our work
with this system and believe we will be able to address both the time spent in the
market and the drawdown shortly, with the help of a few (trend) filters.
VOLUME-WEIGHTED AVERAGE
This system presented us with a couple of interesting choices. When tested using
the stop-loss method, the percentage-stop concept indicated the system would
work best with a stop loss of 0.4 percent, a profit target of 4.5 percent, and a sevenday maximum trade length. The estimated average profit came out to 0.3 percent,
with about 35 percent profitable trades. The ATR concept, on the other hand, indicated the system would work the best with a trailing stop of 1.4 ATRs, a target of
2 ATRs, and a six-day maximum trade length. The estimated average profit per
trade came out to 0.4 percent, with about 45 percent profitable trades.
Stop-loss Version
This is a good illustration of how the very same set of entry signals can produce two
distinctly different types of systems, even though both versions are fairly short-term,
with maximum trade lengths of six and seven days, respectively. Note that for the percentage method, the initial risk–reward relationship going into the trade is more than
12:1 (4.5:0.4). This is not the true and final risk–reward relationship: Given that the
stop is fairly tight, while the target is rather generous, it is reasonable to assume that
most losing trades will be stopped out at the maximum allowed loss, which explains
the relatively high amount of losing trades. Most winners, however, will be stopped out
on the seventh day in the trade, before they reach the target. Assuming the average loser
also equals 0.4 percent, we can estimate the average winner to be 1.6 percent [(0.3 * 1
0.4 * 0.65) / 0.35] for a more accurate risk–reward relationship of 4:1.
We really can’t do the same type of calculation for the ATR concept. The
most obvious reason for this is that we use different measuring sticks for the input
and output variables. Because the inputs are measured in ATRs and the output in
percent, we can’t combine them into one formula, as we just did for the percentage concept. But even if the inputs and output where the same, the numbers for
this system still tell us we cannot use the formula to come up with a more accurate risk–reward relationship.
242
In the case of the ATR method, the stop loss is relatively far away from the
entry price, which means that more trades are likely to get stopped out with a loss
because they’ve reached their maximum allowed trade length. These losses are
likely to fall somewhere between the entry price and the stop loss, but because we
don’t know exactly where, it is impossible—using only the information at hand—
to calculate the average loss and the average winner.
Anyhow, an average profit of 0.4 percent per trade with 45 percent profitable
trades for the ATR concept is better than 0.3 percent per trade with only 35 percent profitable trade for the percent concept. The ATR concept also allows us to
go with two input values (the trade length and the profit target) that are placed
closer to the left-hand corner of each chart, which is where we want them to keep
the standard deviation of the returns as low as possible. The surface charts were
uninformative, so let’s move directly to Table 20.5 and compare it to Table 13.5.
Unfortunately, this system did not benefit much (if at all) from the stops. First, the
average profit per trade is slightly lower in Table 20.5 than in Table 13.5. This negative piece of news is also confirmed by both lower profit and risk factors, and a
lower standard deviation of the returns. The latter is also confirmed by a lower
number of profitable markets. The only positive is a good increase in the percentage of profitable trades.
Moving on to the trailing-stop version of the system, Figures 20.16 to 20.18 provide a good illustration on how to use the surface charts when everything lines up
TAB LE
20.5
Long Only Trade Length
Long only: 1.4 ATR stop loss,
PercProf: 79.37
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
108.21
28.36
52.28
6.21
61,624.43
65,767.56
606.89
774.61
5,436.33
Market
0.11
High:
Low:
136.57
79.84
58.50
46.07
127,391.99
(4,143.13)
1,381.49
(167.72)
6,043.21
(4,829.44)
Portfolio
0.78
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.36
0.15
43,035.37
28.14
14.82
5.82
St. Dev:
High:
0.39
1.76
0.16
0.32
22,579.47
65,614.83
17.31
45.44
2.64
17.46
0.21
6.03
Low:
0.97
(0.01)
20,455.90
10.83
12.18
5.61
CHAPTER 20
Adding Exits
243
nicely. Starting with Figure 20.16, we can see that a profit target 2 ATRs away
from the entry price produces the highest profits, together with a trailing stop
between 2.4 and 2.7 ATRs.
With this information at hand, we move to Figure 20.17, which shows that a
profit target of 2 ATRs also should work well with a trade length ranging from four
to nine days. (We’re trying to avoid the three- and ten-day setting at the beginning
and end of the range.) In both cases, the average profit comes out to approximately 0.35 percent per trade. So now we know that a profit target of 2 ATRs works
well with several different settings for both the trailing stop and the maximum
allowed trade length. It remains to be seen if we can make the maximum trade
length work equally as well with any of the trailing stop lengths suggested by
Figure 20.16.
And what do you know? Looking at Figure 20.18, we see that a maximum
trade length of six days should work well with both a trailing stop of 2.4 ATR and
FIGURE
20.16
Profit target using trailing stop 1.
FIGURE
20.17
FIGURE
20.18
244
CHAPTER 20
Adding Exits
245
a trailing stop of 2.7 ATR. In this case, we will go with the 2.4-ATR stop because
it keeps us closest to the left-hand corner of the chart.
The only not so good thing with the final input values for this system is the
fact that the trailing stop initially is further away from the entry price than the profit target, which in this case results in a risk–reward relationship of approximately
0.8:1 going into the trade (2:2.4). This, of course, is not an ideal situation, but
sometimes we have to work with what we have, so let’s try this system out before
we discard it. Table 20.6 shows the combined results for this version of the system.
When this table is compared to Table 13.5, we see that this version of the system generates a slightly higher average profit per trade, but that it also comes with
a slightly higher risk, as illustrated by a slightly lower risk–reward ratio of 0.83
compared to 0.95 in Table 13.5. The risk and profit factors also are slightly lower
than for the original system. All in all, this indicates that the system is doing very
well on some of the markets, but not so well on others. However, the markets that
are producing a profit also do so with a large percentage of profitable trades,
which results in a total of 54 percent profitable trades for all markets, including
the not-so-profitable ones, a very good number indeed.
HARRIS 3L-R PATTERN VARIATION
This was the only system that did not produce profitable results across all variable
combinations. More specifically, the system did not work well with the ATR concept that has worked so well with the previous three systems.
TAB LE
20.6
Results of Trailing Stop on Value-weighted Averages System
PercProf: 84.13
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
105.89
27.38
54.10
6.23
66,831.69
68,883.10
667.86
804.79
5,576.14
Market
0.12
High:
Low:
133.27
78.51
60.33
47.87
135,714.78
(2,051.41)
1,472.65
(136.93)
6,244.00
(4,908.29)
Portfolio
0.83
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.40
0.43
0.16
0.17
43,617.24
22,329.77
28.18
17.05
15.38
2.73
6.17
0.21
High:
Low:
1.84
0.97
0.33
(0.01)
65,947.01
21,287.48
45.23
11.14
18.10
12.65
6.38
5.95
246
Stop-loss Version
As it turned out, the best version of this system, using the percentage concept, only
managed to produce an average profit per trade of 0.12 percent. However, one
major reason for this is the much shorter average trade length, when compared to
the other three systems tested so far. The best version of the system incorporates
a stop loss of 0.4 percent, a profit target of 3 percent, and a maximum trade length
of four days. Figure 20.19 and Table 20.7 show the results for this version, to be
compared to Table 14.6.
Table 20.7 shows that this latest version of the system has a slightly lower
average profit per trade than its predecessor. That the risk–reward ratio also is
slightly lower than previously also adds to the not-so-good news. However, the situation isn’t as bad as it might seem at first glance, because both the profit and risk
factors are slightly higher, albeit with a higher standard deviation as well. Another
piece of good news comes with this latest version of the system: If you divide the
FIGURE
20.19
Results of stop loss on Harris 3L-R pattern variation.
CHAPTER 20
Adding Exits
247
TAB LE
20.7
Results of Stop-loss on Harris 3L-R Pattern Variation
Long only: 0.4% stop loss,
3% profit target, 4 bars max. trade length
PercProf: 83.08
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
157.95
40.00
37.78
7.68
45,342.07
47,437.17
296.69
324.30
2,915.76
Market
0.10
High:
Low:
197.95
117.95
45.45
30.10
92,779.24
(2,095.09)
620.99
(27.61)
3,212.45
(2,619.07)
Portfolio
0.91
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.38
0.47
1.84
0.91
0.21
0.25
0.46
(0.05)
29,338.37
16,921.27
46,259.64
12,417.10
21.44
15.53
36.97
5.91
10.20
1.91
12.11
8.29
2.74
0.21
2.94
2.53
Average:
St. Dev:
High:
Low:
average profit per trade by the average number of days in a trade, you will find that
it is slightly higher for this version than the previous one. In fact, the good news
is that this value stays above $100 per bar, which means that the average profit per
bar in a trade will be 0.1 percent, given that we invest $100,000 per trade (100 /
100,000 * 100).
If we can be in a trade every trading day of the year, making 0.1 percent per
day, the noncompounded return will be 25 percent per year (0.1 * 250), given an
initial investment of $100,000, which is way more than the long-term average for
the market as a whole. Remember, however, these numbers do not include slippage
and commission. But this is counterweighted by the possibility of compounding
the returns when trading several markets within one portfolio. More about this in
Part 4.
Another piece of good news is that the time spent in the market is much
lower for this version of the system. This increases the possibility of compounding the returns when trading several markets and systems at once. The less time
spent in the market for any specific system–market combination, the more room
we have to diversify. The more systems and markets we can trade, the faster we
can compound our returns.
Basically, what could be said about the stop-loss method of this system also can be
said about the trailing-stop method, except the results for the trailing-stop version
are a tad lower, which Table 20.8 illustrates. Note especially that, despite a higher
248
TAB LE
20.8
Results of Trailing Stop on Harris 3L-R Pattern Variation
Long only: 2.7% trailing stop,
4.5% profit target, 5 bars max. trade length
PercProf: 83.08
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
154.55
37.97
44.29
5.83
47,503.23
49,797.29
316.53
362.77
3,359.87
Market
0.09
High:
Low:
192.52
116.58
50.12
38.45
97,300.52
(2,294.06)
679.31
(46.24)
3,676.40
(3,043.34)
Portfolio
0.87
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.30
0.33
1.63
0.97
0.15
0.16
0.32
(0.01)
33,669.37
17,285.23
50,954.59
16,384.14
24.18
16.13
40.31
8.05
13.11
3.51
16.62
9.61
3.57
0.65
4.22
2.92
Average:
St. Dev:
High:
Low:
average profit per trade, this version of the system calls for a longer maximum trade
length, which will lower the average profit made per bars in trade. The only positive is that the number of profitable trades is slightly higher, at 44 percent.
EXPERT EXITS
Like the Harris system, the expert exits system also worked best using the percentage concept. It would be interesting to examine the differences between those
two systems that worked best using the percentage concept, when compared to
those three systems that worked best using the true-range concept. A few observations can be made right away that could serve as a starting hypothesis for your
own research into this.
One observation is that the systems that worked best with the percentage
concept also are the latest two systems tested, and did best on the short side. It
could be that we are better off using the percentage concept if we would like to
work with identical stop and exit settings for both long and short trades. These two
systems may have worked the best in the bear market simply because there were
plenty of bear markets to test them on.
Another reason why the latest two systems worked best using the percentage
concept could be because they are by far the simplest and most short-term in their
construction, relying on only a few comparisons between the very last bars leading up to the trade. This also results in the shortest average trade lengths. The exact
reason for this, however, I will leave for you to research. You know almost as much
about these systems now as I do.
CHAPTER 20
Adding Exits
249
Stop-loss Version
Using the stop-loss method, the best version of this system incorporated a stop loss
of 0.6 percent, a profit target of 3.5 percent, and a maximum trade length of three
days, which resulted in a very profitable system, indeed. Table 20.9 shows that this
version of the system makes an average profit of $532, with a risk–reward ratio of
1.46. These good numbers are also confirmed by very high profit and risk factors
and very low standard deviations. Note also that the average trade length is less
than three days, including the weekends and holidays, which means that this system will make $200 a day, on average, when in a trade. The percent time spent in
the market also looks low enough to make it possible to combine it with other systems for a well-diversified portfolio.
Table 20.10 shows that the trailing-stop version of this system is not quite as profitable as the stop-loss version, but it isn’t far from it. Note that this version has a
much wider stop loss combined with only a slightly longer average trade length.
Thus, most losses for this version of the system may come because of the tradelength stop. Nonetheless, both versions of the system are definitely among the best
versions tested. It only goes to show what one can do with a very basic entry technique, as long as you keep track of where and when to exit.
TAB LE
20.9
Results of Stop Loss on Expert Exits System
Long only: 0.6% stop loss,
NetProfit
AvgProfit
PercProf: 96.92
Trades
PercWin
ProfitStD
RiskRatio
Average:
195.74
41.19
89,268.37
532.72
St. Dev:
High:
59.54
255.28
6.89
48.08
55,718.56
144,986.93
365.61
898.33
2,957.72
3,490.44
0.17
Portfolio
Low:
136.20
34.30
33,549.81
167.11
(2,424.99)
1.46
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.60
0.43
0.33
0.22
26,910.20
19,000.36
17.66
18.08
13.11
3.44
2.83
0.23
High:
2.03
0.55
45,910.56
35.74
16.55
3.06
Low:
1.17
0.11
7,909.84
(0.41)
9.67
2.60
Market
250
TAB LE
20.10
Results of Trailing Stop on Expert Exits System
Long only: 2.7% trailing stop,
PercProf: 90.77
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
192.15
56.68
46.25
5.37
87,226.75
62,318.27
529.15
388.33
3,321.90
Market
0.15
High:
Low:
248.84
135.47
51.62
40.88
149,545.02
24,908.47
917.48
140.82
3,851.05
(2,792.75)
Portfolio
1.36
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.51
0.38
1.89
1.13
0.26
0.19
0.44
0.07
31,946.18
21,181.11
53,127.29
10,765.07
20.77
20.01
40.78
0.76
16.40
5.30
21.70
11.10
3.58
0.65
4.23
2.93
Average:
St. Dev:
High:
Low:
UNCOMMENTED BONUS STOPS
Because I had to keep the stops fairly basic for the research in this book, here are
a bunch of more complex bonus stops you can experiment with yourself:
{***** Percentage-based Stops *****}
Variables:
StopLoss(4), TrailingStop(2), ProfitStop(25), TargetStop(8), SlowBar(3),
MinBarMove(0.25), MaxLength(10), LongLoss(0), ShortLoss(0), LongTrailing(0),
ShortTrailing(0), TrueLength(0), TrueProfitStop(0), LongProfit(0), ShortProfit(0),
TrueMinBarMove(0), LongTarget(0), ShortTarget(0), TrueSlowBar(0),
TrueNextBar(0), TrueMaxLength(0);
LongLoss = 1 - StopLoss * 0.01;
ShortLoss = 1 + StopLoss * 0.01;
LongTrailing = 1 - TrailingStop * 0.01;
ShortTrailing = 1 + TrailingStop * 0.01;
TrueProfitStop = 1 - ProfitStop * 0.01;
LongTarget = 1 + TargetStop * 0.01;
ShortTarget = 1 - TargetStop * 0.01;
TrueSlowBar = SlowBar - 1;
TrueMinBarMove = MinBarMove * 0.01;
TrueMaxLength = MaxLength - 1;
CHAPTER 20
Adding Exits
251
End;
If StopLoss > 0 Then Begin
If Close < EntryPrice * LongLoss Then
ExitLong ("L.C-Loss") on Close;
If Close > EntryPrice * ShortLoss Then
ExitShort ("S.C-Loss") on Close;
End;
{***** The Stop Loss *****}
ExitLong ("L-Loss") Next Bar at EntryPrice * LongLoss Stop;
ExitShort ("S-Loss") Next Bar at EntryPrice * ShortLoss Stop;
End;
{***** The Trailing Stop *****}
If TrailingStop > 0 Then Begin
ExitLong ("L-Trail") Next Bar at Close * LongTrailing Stop;
ExitShort ("S-Trail") Next Bar at Close * ShortTrailing Stop;
End;
{***** The Profit Protector *****}
If ProfitStop > 0 Then Begin
TrueLength = BarsSinceEntry + 1;
LongProfit = (Highest(Close, TrueLength) - EntryPrice) * TrueProfitStop;
ShortProfit = (EntryPrice - Lowest(Close, TrueLength)) * TrueProfitStop;
ExitLong ("L-Prft") Next Bar at EntryPrice + LongProfit Stop;
ExitShort ("S-Prft") Next Bar at EntryPrice - ShortProfit Stop;
End;
{***** The Profit Target *****}
If TargetStop > 0 Then Begin
ExitLong ("L-Trgt") Next Bar at EntryPrice * LongTarget Limit;
ExitShort ("S-Trgt") Next Bar at EntryPrice * ShortTarget Limit;
End;
If BarsSinceEntry >= TrueSlowBar Then Begin
{***** The Slow-trade Stop *****}
If TrueSlowBar > 0 and OpenPositionProfit < 0 Then Begin
ExitLong ("L-Slow") on Close;
ExitShort ("S-Slow") on Close;
252
End;
{***** The Min-move Stop *****}
If TrueMinBarMove > 0 Then Begin
TrueNextBar = BarsSinceEntry + 2;
ExitLong ("L-Min") Next Bar at EntryPrice *
(1 + (TrueMinBarMove * TrueNextBar)) Stop;
ExitShort ("S-Min") Next Bar at EntryPrice *
(1 - (TrueMinBarMove * TrueNextBar)) Stop;
End;
End;
{***** The Max-length Stop *****}
If MaxLength > 0 and BarsSinceEntry >= TrueMaxLength Then Begin
ExitLong ("L-Time") on Close;
ExitShort ("S-Time") on Close;
End;
End;
{***** True-range Stops *****}
Variables:
StopLoss(2), TrailingStop(1), ProfitStop(25), TargetStop(4), SlowBar(3),
MinBarMove(0.25), MaxLength(10), RangePeriod(20), OneRange(0),
StopRange(0), TrailRange(0), TrueLength(0), TrueProfitStop(0), LongProfit(0),
ShortProfit(0), MinTradeMove(0), TargetRange(0), TrueSlowBar(0),
TrueNextBar(0), TrueMaxLength(0);
TrueProfitStop = 1 – ProfitStop * 0.01;
TrueSlowBar = SlowBar - 1;
TrueMaxLength = MaxLength - 1;
End;
OneRange = AvgTrueRange(RangePeriod);
{***** The Stop Loss *****}
StopRange = StopLoss * OneRange;
ExitLong ("L-Loss") Next Bar at EntryPrice - StopRange Stop;
ExitShort ("S-Loss") Next Bar at EntryPrice + StopRange Stop;
End;
{***** The Trailing Stop *****}
CHAPTER 20
Adding Exits
253
If TrailingStop > 0 Then Begin
TrailRange = TrailingStop * OneRange;
ExitLong ("L-Trail") Next Bar at Close - TrailRange Stop;
ExitShort ("S-Trail") Next Bar at Close + TrailRange Stop;
End;
{***** The Profit Protector *****}
If ProfitStop > 0 Then Begin
TrueLength = BarsSinceEntry + 1;
LongProfit = (Highest(Close, TrueLength) - EntryPrice) * TrueProfitStop;
ShortProfit = (EntryPrice - Lowest(Close, TrueLength)) * TrueProfitStop;
ExitLong ("L-Prft") Next Bar at EntryPrice + LongProfit Stop;
ExitShort ("S-Prft") Next Bar at EntryPrice - ShortProfit Stop;
End;
{***** The Profit Target *****}
If TargetStop > 0 Then Begin
TargetRange = TargetStop * OneRange;
ExitLong ("L-Trgt") Next Bar at EntryPrice + TargetRange Limit;
ExitShort ("S-Trgt") Next Bar at EntryPrice - TargetRange Limit;
End;
If BarsSinceEntry >= TrueSlowBar Then Begin
{***** The Slow-trade Stop *****}
If TrueSlowBar > 0 and OpenPositionProfit < 0 Then Begin
ExitLong ("L-Slow") on Close;
ExitShort ("S-Slow") on Close;
End;
{***** The Min-move Stop *****}
If MinBarMove > 0 Then Begin
TrueNextBar = BarsSinceEntry + 2;
MinTradeMove = MinBarMove * OneRange * TrueNextBar;
ExitLong ("L-Min") Next Bar at EntryPrice +
MinTradeMove Stop;
ExitShort ("S-Min") Next Bar at EntryPrice –
MinTradeMove Stop;
End;
End;
{***** The Max-length Stop *****}
254
If MaxLength > 0 and BarsSinceEntry >= TrueMaxLength Then Begin
ExitLong ("L-Time") on Close;
ExitShort ("S-Time") on Close;
End;
End;
CHAPTER
21
Systems as Filters
You can determine the long-term trend several ways. The most straightforward
way is simply to use your own fundamental and discretionary judgment about
where the economy in general and your stocks in particular are heading, and then
stick to that prognosis over a prolonged period of time. Other ways could be to
trade only in the same direction of a long-term moving average, or some other
indicator suitable for more long-term analysis.
Over the years I proved that this works, in several articles for Futures and
Active Trader magazines, and also in my first book, Trading Systems That Work.
For example, in Trading Systems That Work, I examined 16 different futures markets over the period January 1980 to October 1999. First, I tested all markets 12
times each with a system that entered the market randomly in either direction, and
stayed in the trade for five days. Then I added a 200-day moving average and
altered the rules for the system so that it was allowed to enter randomly only in the
same direction as the long-term trend.
Without the trend filter, only seven markets had an average profit factor
above one, but for none of them could we say with 68 percent certainty that the
true profit factor also would be above one. For all markets combined, trading
without a trend filter, the true profit factor was, with 68 percent certainty, likely
to be found somewhere within the interval 0.88 to 1.12. With the trend filter,
however, all markets but one had an average profit factor above one, and for a
total of nine we also could say that we could be 68 percent sure that the true profit factor, trading with the trend filter, also would be above one. For all markets
combined, the true profit factor could with 68 percent certainty be found in the
interval 1.03 to 1.29.
255
256
In the April 2000 issue of Active Trader magazine, I illustrated the importance of only trading with the long-term trend on the stock market (“Short-term
Strategy,” “Long-term Perspective”). This time, I tested the thirty stocks in the
Dow Jones Index, over the period January 1990 to October 1999. The rules for
trading with and without the trend filter were the same as for the test on the futures
markets, except that those stocks I “only” tested 10 times each. Tables 21.1 and
21.2 show the results of these tests.
TAB LE
21.1
Testing without Trend Filter
Company
PF
St. dev.
% win
St. dev.
3M
Alcoa
1.05
0.99
0.15
0.07
52.52
52.69
2.66
2.27
American Express
AT&T
Boeing
Caterpillar
Citigroup
Coca-Cola
Disney
DuPont
Exxon
General Electric
General Motors
Home Depot
Honeywell
Hewlett-Packard
IBM
International Paper
Intel
Johnson & Johnson
JP Morgan
1.05
0.96
1.08
1.06
0.99
1.08
0.96
1.05
0.92
0.95
1.03
0.94
1.09
1.00
1.00
1.01
1.01
1.02
1.07
0.14
0.22
0.11
0.11
0.12
0.18
0.18
0.21
0.12
0.11
0.12
0.18
0.22
0.18
0.27
0.18
0.11
0.19
0.23
51.28
49.85
51.88
52.84
51.02
51.97
50.73
50.56
50.33
50.10
51.17
50.37
52.53
50.53
50.73
51.89
50.15
51.16
51.69
2.76
4.71
1.42
2.26
2.82
3.32
2.41
2.67
2.57
1.86
2.79
2.10
3.62
1.53
3.16
3.14
2.38
1.61
3.67
Kodak
McDonalds
Merck
Microsoft
0.99
0.89
1.08
0.92
0.18
0.12
0.20
0.13
51.43
49.85
51.58
50.96
2.61
3.15
2.19
2.85
Procter & Gamble
1.02
0.23
50.83
2.39
Philip Morris
SBC Communications
United Technologies
Wal-Mart
1.12
0.98
1.04
1.11
0.20
0.15
0.29
0.28
53.42
50.07
52.34
51.40
2.09
3.41
2.53
3.14
CHAPTER 21 Systems as Filters
TAB LE
257
21.2
Testing with Trend Filter (200-day Moving Average)
Company
PF
St. dev.
% win
St. dev.
3M
Alcoa
0.85
1.00
0.12
0.13
48.14
48.10
2.48
2.12
American Express
AT&T
1.14
1.11
0.16
0.26
53.59
51.70
2.66
2.69
Boeing
Caterpillar
Citigroup
Coca-Cola
Disney
DuPont
Exxon
General Electric
General Motors
Home Depot
Honeywell
Hewlett-Packard
IBM
International Paper
Intel
Johnson & Johnson
JP Morgan
0.91
0.94
1.29
1.01
0.97
0.93
0.91
1.37
0.96
1.29
1.11
1.07
1.22
0.78
1.26
1.17
1.06
0.12
0.22
0.22
0.19
0.20
0.15
0.15
0.25
0.11
0.16
0.10
0.14
0.22
0.14
0.20
0.17
0.14
52.19
50.62
57.01
52.96
52.22
48.39
50.73
55.10
49.61
54.86
54.90
50.96
58.36
48.42
52.39
54.03
51.68
2.54
2.56
3.85
2.68
3.62
3.07
1.22
2.48
2.25
3.05
1.73
1.43
1.75
2.86
2.50
2.84
2.57
Kodak
McDonalds
Merck
Microsoft
Procter & Gamble
Philip Morris
SBC Communications
United Technologies
Wal-Mart
0.96
1.01
1.07
1.49
1.06
1.26
1.01
1.26
1.42
0.16
0.19
0.16
0.41
0.18
0.17
0.20
0.19
0.24
50.70
51.98
57.32
56.52
49.58
55.33
51.24
55.51
58.61
3.38
1.91
3.08
2.61
2.45
2.05
2.44
2.87
3.58
Figure 21.1 shows that without the trend filter, 18 markets had an average
profit factor above one. However, we cannot say that the true profit factor is
above one for any of them, because the one standard deviation will bring the onestandard-deviation boundary below one, when deducted from the profit factor.
Also, 28 markets had more than 50-percent profitable trades, but only three of
them were sufficiently above the 50-percent mark, for us to say that we can be 68
percent sure that the true percentage profitable trades also should be above 50
percent. For all stocks combined, the true profit factor will, with 68 percent
258
certainty, fall somewhere in the interval 0.83 to 1.19, while the true percentage of
profitable trades will, with 68 percent certainty, fall somewhere in the interval
48.48 to 54.05.
In Table 21.2, 21 markets have a profit factor above one, and 19 markets
have a higher profit factor than in Table 21.1. Of all 30 markets, we also now can
say that 11 of them also have a high enough profit factor so that we can be 68 percent sure that their true profit factors will be above one. Using the trend filter, 21
markets also had a higher percentage of profitable trades, as compared to without the filter. Of these 21 markets, for 14 of them, we also can say that we can be
68 percent certain that the true percentage of profitable trades is over 50 percent.
For all stocks combined, the true profit factor will, with 68 percent certainty, fall
somewhere in the interval 0.85 to 1.35, while the true percentage of profitable
trades will, with 68 percent certainty, fall somewhere in the interval 48.77 to
56.69.
Although the test shows that we still can’t be sure that the average profit factor for all stocks will be above one, it still shows that most stocks will benefit from
a trend filter, even as rudimentary and arbitrarily chosen as this one. We still can’t
say with 68 percent certainty that the profit factor for all stocks will be above one
because a few stocks didn’t like this trend filter at all and therefore contributed to
increase the standard deviation of the results.
In the same article, another test showed that it was possible to increase the
performance of a short-term system traded on the S&P 500 futures market, by only
taking the trades in the direction indicated by a 200-day on-balance-volume indicator. In short, this test lowered the number of trades from 332 to 177, while at the
same time it increased the profit factor from 1.21 to 1.56 and the number of profitable trades from 53.31 percent to 58.19 percent.
While the on-balance-volume indicator is one of my favorite trend indicators,
because it incorporates all the concepts of technical analysis (price and volume)
into one simple-to-understand number, the lookback period for this indicator too
was arbitrarily chosen. Plenty of other tests in Trading Systems That Work, on other
futures markets, using other systems and filtering techniques, confirm the importance of always trading with the trend.
That said, this isn’t exactly what this chapter will be about. Yes, we will apply
three different filters to the five short-term systems we have worked with in this
section, the three filters being the more long-term relative strength systems we
introduced in Part 2. However, the major difference between the testing we will do
here and the tests just mentioned is that, for the tests to come, we are not all that
interested in the actual long-term trend of the markets, but rather if the market we
intend to trade shows a greater potential for moving the way we want it to, as compared to one or several other markets. As a consequence of that, we might or might
not trade with the direction of the long-term trend, and at this point I have no idea
what the results will be.
259
As it turned out, this was a very interesting piece of research where very few
of the ten different versions of the five systems—to which we just applied the
stops and exits—did better with the intermediate-term filters. Looking through the
results, there are several possible reasons for this.
Reason number one is that none of the filters is an actual trend filter, but
rather a relative strength filter, which means that we will filter away plenty of good
trading opportunities in good trends, only because the stock in question wasn’t
among the very strongest ones at that particular point in time, despite the fact that
it too was in a good trend. This actually means that we will filter away more good
trades than bad trades. Because during times when the trend goes completely
against the anticipated direction of the trade, the trend filter will still allow a trade
to take place, as long as the stock in question is among the strongest ones, no matter the actual direction of the trend.
Reason number two is that, while each filter might do a good job isolating
the intermediate-term relative strength between the stocks in question, it seems it
isn’t necessarily a good idea to trade the strongest of these stocks in the short term.
In fact, reversing the logic for a few of the filters before trading with a few of the
short-term systems reveals that it actually could be a better idea to trade the weakest stock in a group of stocks, as long as it trends in the right direction. The logic
is as follows: If the trend for all stocks is up, those that seem the most likely to
explode to the upside in the short term are those that have lagged behind in the
intermediate term.
Reason number three is that, the more rules we stack on top of each other
within one single strategy, the fewer the markets that will be able to produce a
profit, simply because the added rules mean curve fitting to more specific market
conditions, which fewer and fewer markets will be able to meet. During the testing, this can show up in a higher average profit factor for the filtered version of
the system because it is doing extremely well on a few markets, which even can
boost the average profit factor for all markets—especially if the winning markets
also trade relatively infrequently, so that the gross profits and losses are relatively
small. At the same time, though, the average profit and number of profitable markets will decrease, because the added rules make an increasing number of markets
unprofitable.
For example, if one market produces a gross profit of $20 and a gross loss of
$10, its profit factor will be 2 (20 / 10), and its total profit and average profit per
trade will both be positive. At the same time, another market produces a gross
profit of $980 and gross loss of $1,020, which results in a profit factor of 0.96
(980 / 1020), and its total profit and average profit will be negative. Looking at the
two markets combined, we see that the average profit factor will be 1.48 [(2 0.96) / 2], suggesting that both markets will trade profitably together. However,
that this will not be the case is revealed by the combined total and average profits,
which will be negative.
260
Reason number four is the order of the systems in the first place. In this case,
we started by adding the stops to all systems and markets, traded in any market
condition. We did so because we wanted the systems to work on average equally
well all the time. However, we could have defined the market condition under
which we want the system to operate first, and then optimized the stops for that
condition only. As it is now, the settings for the stop and exit lengths and times also
are influenced by conditions under which we wouldn’t have traded anyway, given
the filters we just added.
From a practical point of view, this means that most stops, exits, and time
frames probably are a little too tight to be optimal, given the market conditions
under which they are supposed to operate. During the bad periods, the systems try
to make a buck as quickly as possible or stop out a loser as soon as possible.
During good periods, on the other hand (those supposedly identified by the filters), the systems really should make the profits run a little longer and keep the
stops a little further away from the entry price, to give the systems a better chance
to make use of the favorable conditions. They apparently don’t manage to do this
as things are right now.
Aside from these reasons, adding a filter will almost always also reduce the
risk–reward ratio, simply because the filter also reduces the number of trades that
go into the calculation for this system measure. There isn’t much we can do about
that. To achieve smoother returns through diversification, we have to make room
for several systems and markets to be traded simultaneously. To do so we need to
trade each system–market combination less frequently by somehow filtering out
some of the trades. The fewer trades produced by a specific system–market combination, the less we can say about its outcome in the future.
Let’s look through the results for the select system and filter combinations
that we will take with us to the money management analysis in Part 4. Remember
that all systems are long only.
RS SYSTEM NO. 1 AS THE FILTER
Table 21.3 shows that the stop-loss version of the meander system, together with
RS system No. 1 as the filter, didn’t do much worse than the filterless version,
depicted in Table 20.3. In fact, given the anticipated decrease in performance in
general and in the risk–reward ratio in particular, the only true negative is that the
percent of time spent in the market didn’t decrease as much as desired. The meander system definitely has some serious potential.
The same holds true for the trailing-stop versions of the volume-weighted
average system (Table 21.4) and the Harris 3L-R pattern variation (Table 21.5).
The only true negative here is their relatively low risk–reward ratios, compared to
the original versions in Tables 20.6 and 20.8, respectively. One good thing with
these systems, as with the stop-loss version of the expert exits system (Table 21.6),
TAB LE
261
21.3
Meander System Using RS System No. 1 as Filter
Meander system, V.1.0: 1.8 ATR stop loss,
PercProf: 86.67
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
144.58
34.32
52.97
4.41
99,512.31
76,271.48
756.36
623.94
6,790.48
Market
0.11
High:
Low:
178.90
110.26
57.38
48.56
175,783.79
23,240.82
1,380.30
132.41
7,546.84
(6,034.13)
Portfolio
1.21
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.32
0.25
1.57
1.08
0.14
0.11
0.25
0.04
64,199.52
35,052.61
99,252.12
29,146.91
32.83
19.02
51.85
13.80
28.47
4.14
32.61
24.33
8.34
0.25
8.58
8.09
Average:
St. Dev:
High:
Low:
is the relatively little time they spend in the market, which makes plenty of room
for diversification with other systems and markets. Note also that both the meander system and the expert exits systems still have risk–reward ratios well above
one, which means that at least 84 percent of all trading sequences will produce a
profit, statistically speaking.
TAB LE
21.4
Volume-weighted System Using RS System No. 1 as Filter
Volume-weighted average: 2.4 ATR trailing stop,
PercProf: 80.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
61.78
19.62
52.85
8.02
33,372.20
49,494.94
565.68
1,143.89
5,677.57
Market
0.10
High:
Low:
81.41
42.16
60.87
44.83
82,867.14
(16,122.75)
1,709.57
(578.21)
6,243.25
(5,111.89)
Portfolio
0.49
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
1.39
0.15
39,605.78
29.51
8.90
6.13
St. Dev:
High:
0.57
1.96
0.24
0.39
22,762.27
62,368.06
19.87
49.38
2.16
11.06
0.23
6.36
Low:
0.83
(0.09)
16,843.51
9.65
6.74
5.90
262
TAB LE
21.5
Harris 3L-R Path Variant Using RS System No. 1 as Filter
Harris 3L-R pattern variation: 2.7% trailing stop,
PercProf: 75.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
108.78
28.71
42.60
5.16
29,297.27
38,649.73
277.68
472.58
3,530.43
Market
0.07
High:
Low:
137.50
80.07
47.77
37.44
67,947.01
(9,352.46)
750.27
(194.90)
3,808.11
(3,252.75)
Portfolio
0.59
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.25
0.32
1.57
0.93
0.13
0.19
0.32
(0.06)
30,240.42
14,074.59
44,315.01
16,165.83
23.10
13.47
36.57
9.64
9.03
2.36
11.39
6.68
3.49
0.57
4.06
2.93
Average:
St. Dev:
High:
Low:
RELATIVE-STRENGTH BANDS AS THE FILTER
The hybrid system No. 1 probably least liked the filters, no matter which filter it
was teamed up with (Table 21.7). In fact, the only good news is that the percentage of time spent in the market also decreased by approximately 50 percent, to a
tolerable 15 percent (compare with Table 20.1). Other than that, the stop-loss verTAB LE
21.6
Expert Exits System Using RS System No. 1 as Filter
Expert exits: 0.6 % stop loss,
PercProf: 96.67
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
127.75
39.57
43.99
4.83
49,501.30
32,839.33
442.65
362.72
2,950.79
Market
0.15
High:
Low:
167.32
88.18
48.82
39.16
82,340.64
16,661.97
805.37
79.93
3,393.44
(2,508.14)
Portfolio
1.22
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.52
0.40
0.28
0.19
22,920.70
13,920.08
15.94
9.66
7.34
1.83
2.44
0.08
High:
Low:
1.92
1.11
0.47
0.08
36,840.78
9,000.62
25.60
6.28
9.17
5.51
2.52
2.36
TAB LE
263
21.7
Hybrid System Using Relative-strength Bands as Filter
Hybrid system No. 1: 1 ATR stop loss,
Average:
St. Dev:
High:
Low:
Average:
St. Dev:
High:
Low:
PercProf: 72.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
97.00
35.80
48.31
7.09
28,607.08
53,259.36
295.41
707.02
4,275.30
Market
0.07
132.80
61.20
55.39
41.22
81,866.44
(24,652.28)
1,002.42
(411.61)
4,570.71
(3,979.90)
Portfolio
0.42
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.24
0.39
1.62
0.85
0.10
0.18
0.28
(0.08)
34,905.87
25,342.23
60,248.10
9,563.64
26.43
16.00
42.42
10.43
15.02
3.91
18.93
11.12
4.87
0.33
5.20
4.54
sion of this system lost as much as one-third of its average profit per trade and
two-thirds of its risk–reward ratio. The number of profitable markets also
decreased from over 90 percent to a more modest 72 percent.
However, reversing the rules for many of the filters before applying them to
this system improved the performance for many of the new system–filter versions
considerably. This is not shown, but you can try it yourself on a system that actually does best when trading the weakest stock in a group of stocks (according to
our second reason why an intermediate-term relative-strength filter might not
always function as anticipated).
The stop-loss version of the meander system continued to do fairly well with
the relative-strength bands as filters. If you compare this version of the system, in
Table 21.8, with the ones in Tables 20.3 and 21.3, you will find that this version
of the system actually had both the highest average profit per trade and the least
time spent in the market of all three versions. A much lower risk–reward ratio of
0.76 is, however, an indication that we cannot be as sure about this version’s future
performance as we can of the others. The time spent in the market is also a little
too high for optimal diversification possibilities.
The trailing-stop version of the volume-weighted average system also holds
up well together with the relative-strength bands as a filter. Comparing Table 21.9
with Tables 20.6 and 21.4, we can see that this version doesn’t fall too far behind
the original version in Table 20.6, having an average profit per trade only some 5
percent lower and a much higher risk–reward ratio than the version in Table 21.4.
The stop-loss version of the Harris 3L-R pattern variation, in Table 21.10, is a
good example of a system–filter combination that boosts the profit factor despite a
264
TAB LE
21.8
Meander System Using Relative-strength Bands as Filter
Meander system, V.1.0: 1.8 ATR stop loss,
PercProf: 76.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
94.20
36.77
52.95
6.27
61,158.69
66,828.26
848.19
1,112.10
6,144.18
Market
0.11
130.97
57.43
59.22
46.67
127,986.95
(5,669.58)
1,960.29
(263.90)
6,992.38
(5,295.99)
Portfolio
0.76
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.39
0.44
1.83
0.95
0.16
0.18
0.35
(0.02)
39,925.46
18,362.82
58,288.28
21,562.64
29.14
16.54
45.68
12.59
24.06
4.66
28.71
19.40
8.23
0.53
8.76
7.70
Average:
St. Dev:
High:
Low:
Average:
St. Dev:
High:
Low:
general decrease of performance, compared to trading without the filter. In this case,
the profit factor comes out to 1.52, compared to 1.38 in Table 20.7, while, for example, the risk–reward ratio is more than cut in half. The same goes for the trailing-stop
version of the same system, in Table 21.11. Although, in this case, given that a small
deterioration of performance because of the filter was expected, it’s almost fair to say
that the filter version of this system is doing better than its predecessor, in Table 20.8.
TAB LE
21.9
Volume-weighted System Using Relative-strength Bands as Filter
PercProf: 69.57
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
37.52
19.00
56.17
9.81
14,106.93
24,036.62
639.20
1,009.94
5,309.69
Market
0.09
High:
Low:
56.52
18.52
65.97
46.36
38,143.55
(9,929.70)
1,649.15
(370.74)
5,948.89
(4,670.48)
Portfolio
0.63
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.36
0.55
0.12
0.20
25,606.39
12,433.08
20.93
11.55
7.49
2.89
6.18
0.34
High:
Low:
1.91
0.80
0.32
(0.08)
38,039.47
13,173.31
32.48
9.38
10.38
4.60
6.53
5.84
TAB LE
265
21.10
Harris 3L-R Pattern Variation Using Relative-strength Bands as Filter
Harris 3L-R pattern variation: 0.4% stop loss,
PercProf: 68.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
65.32
28.55
37.32
10.77
17,490.02
31,467.95
250.19
563.44
2,603.15
Market
0.09
High:
Low:
93.87
36.77
48.09
26.54
48,957.97
(13,977.94)
813.63
(313.25)
2,853.34
(2,352.96)
Portfolio
0.44
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.52
0.85
2.37
0.67
0.25
0.47
0.72
(0.21)
17,136.27
11,128.15
28,264.42
6,008.13
14.77
10.49
25.27
4.28
5.86
1.35
7.20
4.51
2.78
0.30
3.09
2.48
Average:
St. Dev:
High:
Low:
The stop-loss version of the expert exits system using the relative-strength
bands as a filter, in Table 21.12, also is a good example of a system–filter combination that increases performance enough on a few markets to increase the
combined profit factor, but not enough to increase the average profit per trade to
compensate for a decreased performance in many of the other markets. If we compare this version of the system to those in Table 20.9 and 21.6, we can see that
TAB LE
21.11
Harris 3L-R Pattern with Trailing Stop Using Relative-strength Bands as Filter
Harris 3L-R pattern variation: 2.7% trailing stop,
PercProf: 64.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
63.40
26.95
46.02
8.53
19,020.12
34,674.05
307.22
570.95
3,096.72
Market
0.10
High:
Low:
90.35
36.45
54.55
37.48
53,694.17
(15,653.93)
878.17
(263.73)
3,403.94
(2,789.50)
Portfolio
0.54
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.39
0.63
0.17
0.29
18,830.92
10,629.65
16.03
10.14
7.51
2.14
3.68
0.83
High:
Low:
2.03
0.76
0.46
(0.11)
29,460.57
8,201.27
26.16
5.89
9.65
5.37
4.51
2.85
266
TAB LE
21.12
Expert Exits System Using Relative-strength Bands as Filter
Expert exits: 0.6% stop loss,
Average:
St. Dev:
High:
Low:
PercProf: 88.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
82.60
33.57
44.77
11.55
30,342.81
32,531.17
363.19
447.60
2,634.63
Market
0.15
116.17
49.03
56.33
33.22
62,873.98
(2,188.35)
810.79
(84.42)
2,997.82
(2,271.44)
Portfolio
0.81
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.66
0.77
2.43
0.88
0.29
0.33
0.62
(0.05)
16,355.26
12,780.59
29,135.84
3,574.67
14.12
12.57
26.69
1.56
6.71
1.97
8.69
4.74
2.47
0.09
2.56
2.37
Average:
St. Dev:
High:
Low:
despite the fact that this version has the highest profit factor, it still has the lowest
average profit per trade and risk–reward ratio. A lower percentage of profitable
markets traded also is an indication of the same problem: Namely, that it works
very well on a few markets, but not so well in others, thus causing an overall deterioration of the performance.
ROTATION AS THE FILTER
Tables 21.13 and 21.14 (to be compared to Tables 20.2 and 20.4, respectively)
show the trailing-stop versions of the hybrid and meander systems, respectively,
using the rotation system as a filter. In both instances, these versions of the systems don’t do as well as the originals, although the meander system isn’t doing too
badly, given the fact a slight depreciation of performance was to be expected.
Again, the largest negative for the meander system is that it spends a little too
much time in the market for optimal diversification possibilities. For the hybrid
system, however, the situation looks less tantalizing. Just as the version of this system depicted in Table 21.7, this version, too, has lost approximately one-third of
the value of its average trade and about two-thirds of its risk–reward ratio.
The performance summary for the trailing-stop version of the volumeweighted average system in Table 21.15 gives rise to another interesting observation: The same short-term system can behave very differently, only because the
logic behind the stops and exits changes. If you look at Tables 21.4 and 21.9, they
too represent the trailing-stop version of the system. The filter is the only difference among these three tables. What is interesting, however, is what is not shown
TAB LE
267
21.13
Hybrid System Using Rotation as Filter
Hybrid system No. 1: 1.2 ATR trailing stop,
PercProf: 66.67
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
89.46
41.84
42.95
6.64
26,583.22
46,784.46
285.47
695.78
4,273.36
Market
0.08
131.30
47.62
49.59
36.31
73,367.68
(20,201.24)
981.25
(410.31)
4,558.83
(3,987.90)
Portfolio
0.41
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.34
0.55
1.89
0.79
0.16
0.27
0.43
(0.10)
30,883.59
19,786.34
50,669.94
11,097.25
24.18
17.34
41.53
6.84
13.78
4.29
18.07
9.49
4.98
0.27
5.25
4.71
Average:
St. Dev:
High:
Low:
Average:
St. Dev:
High:
Low:
in these tables: Namely, the terrible results produced by the stop-loss version of
this system, no matter which filtering technique it was teamed up with.
For example, Table 21.15 shows that this version of the system has an average profit of close to $500 and a risk–reward ratio of 0.5. The stop-loss version,
on the other hand (not shown), ended up with an average profit per trade of $176,
even though it too had an average trade length of about six days and a risk–reward
ratio as low as 0.18, which was the lowest one in the entire test.
TAB LE
21.14
Meander System Using Rotation as Filter
Meander system, V.1.0: 2.7 ATR trailing stop,
PercProf: 80.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
71.36
37.07
51.78
6.15
39,375.24
48,763.34
707.74
1,048.08
6,188.83
Market
0.09
108.43
34.29
57.93
45.64
88,138.58
(9,388.10)
1,755.82
(340.33)
6,896.57
(5,481.08)
Portfolio
0.68
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.32
0.45
0.14
0.17
37,021.84
16,271.10
24.83
11.64
20.42
6.79
9.55
0.68
High:
Low:
1.78
0.87
0.31
(0.04)
53,292.94
20,750.73
36.47
13.18
27.21
13.63
10.23
8.87
Average:
St. Dev:
High:
Low:
268
TAB LE
21.15
Volume-weighted Averages System Using Rotation as Filter
PercProf: 65.22
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
32.09
17.49
54.44
10.08
11,369.15
26,040.11
491.88
979.71
4,787.07
Market
0.08
High:
Low:
49.58
14.59
64.52
44.37
37,409.26
(14,670.95)
1,471.59
(487.82)
5,278.95
(4,295.19)
Portfolio
0.50
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
1.43
0.80
2.23
0.62
0.15
0.30
0.45
(0.15)
20,580.19
12,290.52
32,870.71
8,289.68
17.79
11.35
29.13
6.44
6.45
3.26
9.71
3.19
6.24
0.36
6.60
5.88
Average:
St. Dev:
High:
Low:
The average profit per trade for the stop-loss version of the Harris 3L-R
pattern variation isn’t much to brag about either. The difference is, however, that
this system spends less than three days in the market per trade, which makes its
daily return much higher than for a system with the same average profit but more
days in a trade. But even so, comparing Table 21.16 with Tables 20.7 and 21.10,
it’s easy to see that pairing the system with rotation as the filter has deteriorated
TAB LE
21.16
Harris 3L-R Pattern Variation Using Rotation as Filter
Harris 3L-R pattern variation: 0.4% stop loss,
PercProf: 68.00
Trades
PercWin
NetProfit
AvgProfit
ProfitStD
RiskRatio
Average:
St. Dev:
53.48
27.30
35.50
10.26
9,741.54
24,440.34
166.28
471.66
2,499.11
Market
0.07
High:
Low:
80.78
26.18
45.77
25.24
34,181.88
(14,698.81)
637.93
(305.38)
2,665.39
(2,332.83)
Portfolio
0.35
ProfitFactor
RiskFactor
MaxDD
PercDD
PercTime
AvgLength
Average:
St. Dev:
1.39
0.73
0.19
0.42
15,278.38
10,931.42
13.86
11.05
4.66
1.58
2.77
0.28
High:
Low:
2.12
0.66
0.61
(0.23)
26,209.79
4,346.96
24.92
2.81
6.24
3.08
3.05
2.49
269
performance quite a bit. Again, the risk–reward ratio is almost one-third the size
of the original system, and the average profit per trade is cut in half. And by now,
perhaps, the time spent in the market is a little too low to make the results reliable
for real-life trading on unseen data.
Let’s round off by looking at two more versions of the expert exits system.
Table 21.17 shows the results for the stop-loss version of the system, to be compared with Tables 20.9, 21.6, and 21.12. This system has a very high profit factor,
which means that it probably trades really well on a few markets. Unfortunately,
the high profit factor also is accompanied by the lowest average profit per trade
and risk–reward ratio for all stop-loss versions looked at in this test, although
they’re not as low as for the trailing-stop version in Table 21.18 (to be compared
with Table 20.10). In both cases, however, the average profit per trade is still very
good, given the short average trade length of these systems.
CHAPTER
22
Variables
Most of the time, when building a system, we talk about making the system
robust, meaning it should be as little curve fitted as possible to increase its chances
of holding up in the future as well as it has in the past or when developed.
However, just using one word for this important consideration—the word robust—
is not enough if we want to get a firm grip on how to go about increasing our
chances for future success. If you ask me, I think there are at least three things we
need to consider, all of which fit within the term robust, as we have used it so far.
Instead of just talking about robustness, I would like to propose that we talk about
robustness, stability, and consistency. Let’s start with the term stability, which is a
concept we’ve stressed throughout Part 3.
Stability means that the system should work equally as well, on average and
over time, using several different variable settings. For example, if you use a nineday moving average for a system, there is no way for you to find out in advance if
you might have been better off with a 10-day average over a certain time period.
If that would have been the case, your nine-day setting should not have worked that
much worse, and definitely not have produced catastrophic results, whereas the
10-day setting would have shown a profit. In the long run and over several subperiods, it should not have mattered that much which of the two settings you would
have gone with.
Another example is when the best variable setting, in hindsight, turned out to
be way off from the one you used. In that case, the best setting might have resulted in a decent profit, but you suffered a rather severe drawdown. That drawdown
should not, however, have been of such magnitude that it forced you out of the
game. The best way to assure stability, as I have defined it here, is to make the sys271
272
tem as broad in scope as possible, work with as few optimizable variables as possible (preferably more than three), and avoid aiming for the stars when it comes to
the performance of the system. A small but steady average profit per trade, resulting in modest profit and risk factors and high risk–reward ratios, is the way to go.
All the analysis we did when looking for the optimal and on average bestworking stops really was to assure stability. We did this using several surface
charts, which helped us compare several input combinations with each other and
find a combination that was surrounded by other combinations, that produced similar results, or at least not results that were catastrophically different.
A robust system is a system that works equally as well, on average and over
time, on several different markets and market conditions. For example, if you use
a nine-day moving average on Microsoft, you should be able to use a nine-day
moving average on General Electric as well without running the risk of being
ruined. Maybe a nine-day setting has worked much better on Microsoft historically, but you must test the system in such a way so that you can trust it on General
Electric as well. At the very least, you should feel confident that if and when
Microsoft starts to behave as General Electric has in the past, you should still be
left with plenty of time to observe and correct.
The two markets might not always be profitable with this setting and General
Electric might only be so under very special conditions (such as a prolonged bear
market). But when these conditions do occur, you want to be prepared. The price
you pay for being this prepared is to allow yourself to lose a little trading General
Electric during normal conditions, and perhaps not make as much on Microsoft as
you could have using the optimal setting for Microsoft, because the nine-day setting you’re working with is the one that works best on average over several markets. The robustness of each system has been examined using the performancesummary tables throughout the book, especially when we also compared the average profit per trade with the risk–reward ratio.
But it’s also fair to say that we looked at each system’s consistency, or how well
the system is likely to perform in several continuous and well-defined time periods,
such as quarterly or yearly. It all depends on how you look at it. If you look at each
series of trades on a specific market as only that, then you are evaluating robustness.
But if you look at each series of trades without taking into consideration where and
when they were produced, then you evaluate the system’s consistency.
There also is another way to research and analyze consistency. Once you’ve
decided on your basic entry and exit rules, and tested the system over several markets to make sure it works equally as well, on average, over several types of market conditions (uptrends, downtrends, low–high volatility periods, etc.), there is
one more thing you can do to make sure the results aren’t just a fluke. So far, a
trading sequence has contained trades only from one market. In real life, however,
a trading sequence over a certain period of time can hold trades from several markets. There is also no saying in what order these trades will occur.
CHAPTER 22
Variables
273
Even if we assume that one or several trading sequences on different markets
give an accurate picture of how the trades will be distributed in the future, in
regard to the relative amount of winners and losers and all the shapes and forms
they can take, there is still no saying that a certain-sized winner will be followed
by a certain-sized loser, or that there won’t be more than a certain number of losers in a row. In real-life trading on unknown data, anything can happen by pure
chance.
To prepare for that, you need to take all the generated trades and scramble
them around, then pick one trade at a time, at random, to create one or several new
trading sequences, based on the original trades from one or several markets or systems. The reasoning behind this analysis is that if the system is robust and stable,
it will continue to produce trades similar to those already generated, with the only
significant difference being the sequence of these trades and how they are positioned in relation to each other.
To collect all your trades in one bag, so to speak, you can use the following
piece of TradeStation code, which simply exports the end result of each trade into
a text file, where all trades will be stored in one column.
{Robustness export, with Normalize(True). Set RobustnessSwitch(True).}
Variable: RobustnessSwitch(True);
If RobustnessSwitch = True Then Begin
Variables: RobNameLength(0), RobFileString(""), ResultString(""),
EndTrade(0);
RobNameLength = StrLen(GetStrategyName) - 6;
RobFileString = "D:\BookFiles\RobustTest-" + RightStr(GetStrategyName,
RobNameLength) + "-" + RightStr(NumToStr(CurrentDate, 0), 4) + ".csv";
End;
EndTrade = TotalTrades;
If EndTrade > EndTrade[1] Then Begin
ResultString = NumToStr(PositionProfit(1), 2) + NewLine;
FileAppend(RobFileString, ResultString);
End;
End;
Once the trades are collected, they can be pasted into an Excel spreadsheet,
which has been prepared for the scrambling and the random picking of all trades,
to form as many new and randomly created trading sequences as you wish. Figures
22.1 to 22.3 show what parts of such a spreadsheet could look like. Let’s look at
Figure 22.1, which shows a small part of a subsheet named “Data.” The trades used
here have nothing to do with the systems tested in this book, and for this analysis
274
FIGURE
22.1
Excel spreadsheet showing randomly selected trades (data subsheet).
FIGURE
22.2
Excel spreadsheet showing randomly selected trades (tables subsheet).
FIGURE
22.3
Excel spreadsheet showing randomly selected trades (equations).
CHAPTER 22
Variables
275
I will not go through all the systems tested, but simply describe the process so that
you can do it yourself on your own systems, later on.
Column A, in Figure 22.1, contains all the historical and hypothetical trades,
copied and pasted from the comma-separated text file they were exported to with
the help of the export function. (Before you copy the trades into column A,
remember to erase any old data you might have saved in column A from the last
time you used the spreadsheet.)
Column C holds an adjusted value for each trade. Depending on whether the
individual trade is a winner or loser, its outcome can be adjusted downwards or
upwards, respectively, to minimize the effect of winners or losers that are deemed
too large. This is a useful feature if you’d like to make sure the results aren’t too
dependent on any exceptionally large winners or losers (especially the winners).
The specified levels can be set in cells D3 and D4 in the subsheet “Tables” (see
Figure 22.2). If the system still produces profitable random trading sequences with
the value in cell D3, in subsheet “Tables” set to one or two standard deviations, it’s
even more likely it will continue to work in the future, and perhaps even be better
than expected, because the exceptionally large winners now come as happy surprises instead of necessary life savers.
The formula in cell C3 in Figure 22.1 looks like this:
IF(A3>0,MIN(A3,Tables!F$4),MAX(A3,Tables!F$5))
Copy the formula in cell C3 all the way down to the last row containing a
trade in column A.
Columns E to X hold randomly picked trades from column C.
The formula in cell E3 looks like this:
INDEX($C:$C,RANDBETWEEN(1,Tables!$D$2))
Copy it 20 columns to the right and 200 rows down, to create 20 random
trading sequences with 200 trades each (or 200 random trading sequences with 20
trades each; you can look at it both ways) The formula will pick a trade at random
from column C.
In Figure 22.2, the subsheet “Tables” contains a few basic values and formulas. The number of trades in columns A and C in subsheet “Data” is typed into
cell D2. The number of standard deviations that should not be surpassed by the
winners and losers are typed into cells D3 and D4. The average profit per trade,
based on the data in column A, subsheet “Data,” is calculated in cell F2 [formula:
AVERAGE(Data!A:A)]. The standard deviation of the data in column A, subsheet “Data,” is calculated in cell F3 [formula: STDEV(Data!A:A)]. The actual
values not to be surpassed by the data in column C, subsheet “Data,” are calculated in cells F4 and F5 [formulas: F2D3*F3 and F2D4*F3]. Note that these
cell references go into cell C3 in subsheet “Data.”
276
Figure 22.3 shows some of the equations needed to calculate most of the statistics that can be derived from this analysis. In this case, the data are calculated
for 200 trades in 20 sequences. A similar set of calculations is done to calculate
the statistics for 20 trades in 200 sequences. All the calculations in cells E202 to
E213 are copied 20 cells to the right, to cells X202 to X213.
Cell E202 calculates the average profit per trade according to the formula
AVERAGE(E1:E200).
Cell E203 calculates the standard deviations of profits according to the formula STDEV(E1:E200).
Cell E204 calculates the risk-adjusted return according to the formula
E202/E203.
Cell E206 calculates the gross profit according to the formula
SUMIF(E1:E200,">0",E1:E200).
Cell E207 calculates the gross loss according to the formula
SUMIF(E1:E200,"<0",E1:E200).
Cell E208 calculates the profit factor according to the formula
E206/ABS(E207).
Cell E210 calculates the number of winning trades according to the formula
COUNTIF(E1:E200,">0").
Cell E211 calculates the percentage of winning trades according to the formula E210/200*100.
Cell E212 calculates the number of losing trades according to the formula
COUNTIF(E1:E200,"<0").
Cell E213 calculates the risk factor according to the formula
(E206+E207)/ABS(E207/E212*200).
With all the calculations in place we can set up a couple of tables resembling
those we used during the initial system testing, based on the data derived by the
large export function, described in Part 2. Table 22.1 shows that of all 200 trading
sequences holding 20 trades each, used for this example, 75 percent tested profitably. The average profit per trade came out to 448.21, and the profit factor came
out to 2.30.
Table 22.2, on the other hand, shows that of all 20 trading sequences, holding 200 trades each, 95 percent came out profitable. The average profit per trade
came out to 448.21, and the profit factor came out to 1.77. Note that the average
profit per trade is exactly the same in both tables, because we’re using exactly the
same randomly deducted trades. But even if we’re using the exact same trades, a
higher percentage of profitable sequences occurs in Table 22.2 than in Table 22.1.
The standard deviations for the average profit per trade, and the profit and risk factors also are much lower in Table 22.2. How can this be? The answer lies in the
CHAPTER 22
Variables
TAB LE
277
22.1
All 200 Trading Sequences Holding 20 Trades Each
20 trades, 200 sequences
Average:
St. Dev:
Trades
NetProfit
AvgProfit
ProfitStD
RiskRatio
20.00
8,964.21
12,829.55
448.21
641.48
2,734.62
Market
0.14
21,793.76
(3,865.35)
1,089.69
(193.27)
3,182.83
(2,286.41)
Portfolio
0.70
PercWin
ProfitFactor
RiskFactor
MaxDD
FlatTime
50.38
11.91
62.29
38.46
2.30
1.97
4.26
0.33
0.50
0.72
1.22
(0.22)
7,284.10
4,359.14
11,643.24
2,924.96
10.31
5.36
15.66
4.95
High:
Low:
Average:
St. Dev:
High:
Low:
PercProf: 75.00
number of trades in each sequence. The more trades used for the calculations, the
more sure we can be that the calculated averages are close and accurate estimates
of the true averages, and the more trades used, the closer each trading sequence
will be to the averages for that amount of trades.
Figure 22.4 shows how the equity can vary over 20 randomly picked trades
for 200 different trading sequences. Basically, the end result can be all over the
place, and although the expected net profit over one sequence is $8,964, it can eas-
TAB LE
22.2
All 20 Trading Sequences Holding 200 Trades Each
200 trades, 20 sequences
Average:
St. Dev:
PercProf: 95.00
Trades
NetProfit
AvgProfit
ProfitStD
RiskRatio
200.00
89,642.05
44,490.38
448.21
222.45
2,906.93
Market
0.15
134,132.44
45,151.67
670.66
225.76
3,355.14
(2,458.72)
Portfolio
2.01
ProfitFactor
RiskFactor
MaxDD
FlatTime
High:
Low:
PercWin
Average:
50.38
1.77
0.37
22,625.23
60.70
St. Dev:
High:
4.54
54.92
0.45
2.22
0.20
0.57
8,068.98
30,694.20
29.93
90.63
Low:
45.83
1.32
0.17
14,556.25
30.77
278
FIGURE
22.4
Equity variation over the randomly picked trades.
ily vary between a profit of $100,000 and a loss of $50,000. Most likely, however,
you will end up somewhere in the interval plus/minus one standard deviation away
from the mean, which should hold approximately 68 percent of all outcomes. But
what happens if one trading sequence ends up with a loss of close to $50,000? Is
that an indication that the loss will be $100,000 after two trading sequences?
No, it is not. It can happen, but it is unlikely that we will lose as much a second time. To understand why this is, we need to remember that two trading
sequences of 20 trades each also equal one trading sequence of forty trades, and
that the more trades in a sequence, the closer its average profit per trade will be to
the true average profit for the system over an infinite number of trades. Of course,
there are no guarantees and a system can simply cease to work at any time, but as
long as the system delivers results within its statistical confines, no such conclusions can be made.
Figure 22.5 shows one trading sequence that shows a loss of close to $75,000
after about 40 trades. However, even this initially really bad sequence eventually
turned around to end up with a final profit very close to the estimated average.
Note that if you start to trade this system today, you can expect to make approximately $175,000 over 200 trades. But if after 200 trades your net profit is only
CHAPTER 22
FIGURE
Variables
279
22.5
Loss of close to $75,000.
$100,000, which is just above the lower one-standard-deviation boundary, there is
nothing wrong with the system. It just so happened that you caught a sequence of
trades with a lower average profit per trade than could have been expected from
the historical estimate, based on 20 such sequences.
In fact, more than every third trading sequence will produce a profit between
the average expected profit and its lower one-standard-deviation boundary, and
about every fifth trading sequence will produce a profit that is lower still. And
every so often (perhaps every 50th sequence or so) there will even be a loss. Also,
the fewer the trades used to calculate the average profit per trade, the more likely
it is that that average is negative. Figure 22.5 shows that still plenty of trading
sequences are left in negative territory after 50 trades or so, and that it takes some
120 trades before the last sequence turns positive. The longer the sequence, however, the closer each sequence will be to the estimated average profit.
Similarly, a system that produces better than expected results (as indicated by
the estimated average profit per trade) still works as it should: you just happened
to luck out with a couple of extraordinarily good trades over a period. The most
dangerous thing you could do at this point is to increase your positions in the belief
that the system has become more robust and reliable. Look at the two sequences
280
in Figure 22.5 that have the best results after some 110 trades. They both start to
move downward from there to get closer to the estimated average profit over 200
trades. What if you had decided to double your positions for these trading
sequences after 110 trades? The drawdowns would have been twice as steep as
they now appear in Figure 22.5.
So the question still remains: If the final outcome for one trading sequence
can vary this much with the system still working as it should, how do we decide
when a system’s inherent characteristics change to the better or worse? (A system
changing to the better, or seemingly better, without us knowing is not a good thing
either. The very same reasons that now make us richer than trolls could be what
ruin us in the end, because we haven’t adjusted the position size of the trades to
accommodate for the new circumstances.)
This is a very difficult question to answer, and I feel I really don’t have the
experience to do it. Nonetheless, I would say that if a system performs way out of
what could be expected (say more than two standard deviations away from the estimated mean) over at least two reasonable, long sequences of trades, it’s reasonable
to assume that something has changed so that the estimated statistics can no longer
be trusted. It may be that you did something wrong from the beginning when constructing the system, or the assumptions on which the system is based no longer
are valid.
Unfortunately, however, I have a gut feeling that most systems get discarded
way before this happens and while the system is still working as it should, simply
because the trader had no idea that the system could produce the type of drawdown
numbers it eventually did. Hence, he starts trading it way undercapitalized.
Analyzing the systems for consistency could help you get a better feel for what
types of drawdowns your systems are most likely to generate, given the statistical
distribution of the trades. With this information at hand, you should not have to be
forced out of the game, despite a good system but because of lack of capital.
CHAPTER
23
Evaluating Stops and Exits
P
art 3 started with a discussion of the distribution of the trades and how it
changes with alterations to the stop and exit levels of the system. Altering the stops
and exits ever so slightly can alter the characteristics and results of a system very
drastically. Therefore, to be prudent, one should really start the entire research
process anew for every little change made to the system. Also, because even the
smallest of changes will add or wash away trades, alter flat times, and move drawdown periods around, one cannot use historical real-life trades and performance
summaries as a base for this type of analysis.
Ideally, a trade should only have two possible outcomes: A loser of a specific size or a winner of a specific size. This is almost never the case, and the number of possible outcomes still is infinite, which produces the money management
consequences we deal with in Part 4. Nonetheless, making a serious effort to keep
the number of possible outcomes as low as possible is one of the hallmarks of a
good trader. In fact, this analysis showed that a normal distribution of the trades is
a sign of sloppy trading, in which we let the trades behave as they wish once we
have entered the market. It is not the distribution of the individual trades that
should be normal, it is the monthly results, or the results over several similar time
frames, that should be normal.
We also learned that the most important thing isn’t to increase the value
of the average trade all by itself, but rather to increase it in relation to the standard deviation of all trades. As long as the average profit per trade remains
large enough to make trading worthwhile, it could be a good thing to lower the
average profit per trade as long as the insecurity of the outcome is lowered to a
larger degree. If we manage to do this, we can increase the dollar returns sim281
282
ply by putting on larger positions, possible thanks to the increased security of
the outcome.
To limit the possible outcomes for a trade, we need to think about the reasons
to exit the trade. Basically, there are four different reasons why we should no
longer stay in a trade. Of the four reasons to exit, two reasons are price-based and
two are time-based. Many times the reasons and methods intertwine, which makes
it all the more important to know what you’re doing.
The most obvious reason to exit is to limit a loss in a trade that goes against
us. For most traders this is easier said than done, and many times when we are limiting a loss, we are doing so at the least opportune moment. It is important that the
loss is taken immediately and where it’s supposed to be taken according to the
strategy rules, so that we can free up the money quickly, put it to use elsewhere,
and leave all bad trades behind us as quickly as possible. Remember that the most
important thing isn’t to have as many winning trades as possible, but rather as
many winning time periods as possible. The best way to achieve that is to cut the
losers as soon as possible, so that we are left with as much time and money as possible to achieve that goal for each time period.
The second reason to exit is to make the most out of a favorable move and
take a profit. Basically, there are two ways to lock in a profit. The most straightforward method is to take the profit with a limit order as soon as it reaches a predefined level. This is a good way to keep the standard deviations of the outcomes
to a minimum. If, in hindsight, it turned out you exited the market prematurely,
you are always free to enter again in this or any other market. The second way to
lock in a profit is to apply a trailing stop slightly below the current price (above
for a short trade). In this way you give back some of the open profit, but you also
give the trade a chance to capture that part of the move a profit target might have
kept you out of.
The third reason to exit is after it is fair to assume the market has discounted the reason that triggered the trade in the first place. To measure this, we need
to get a feel for both the time horizon and magnitude of the moves the system is
most suited to capture. To calculate an exact number of bars to stay in a trade can
be very difficult, and it will alter depending on what type of system you have.
However, a rule of thumb is that a short-term system should not stay in a trade any
longer than the amount of historical data going into the system calculations to trigger the move.
For example, if your system makes use of five days of historical data to calculate the pattern or indicator that triggers the entry, in essence what you have told
yourself is that, in this particular case, the market has a memory of five days—
looking further back in time won’t improve the results for this entry technique.
Therefore, if the market has a five-day memory going into the trade, it only makes
sense it should have a five-day memory leading out of the trade, on average and
over a large number of trades.
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283
A profit target also could be used as an end-of-event exit. This happens when
the anticipated magnitude of the move is reached before the maximum allowed
trade length. In that case, it is not unlikely that the market has overextended itself
in the short run, and it could be a good idea to take a profit with a limit order, and
then enter anew after the market has retraced parts of that move.
The fourth reason is that the money invested in the trade could be put to better use elsewhere, no matter the performance of this trade. Obviously this is the
case with a trade that goes against us, but this also could be a good reason to exit
a winner, if you also monitor and trade several other markets and systems. If
you’re in a slow winner, this could be a difficult exit to execute, but remember that
your research has told you what to expect from a trade. While there is no way to
know how a future trade will develop, at least you have a clear picture of what you
want out of it, and while a future trade still has to prove itself, a slow trade already
has proved itself to be just that—a slow trade.
The most straightforward way to calculate where to place your stops and
exits is to calculate the most opportune percentage distances from the entry price.
The major advantage with this method is that it doesn’t add any new optimizeable
variables that complicate the rulings for the system and detract from the robustness and reliability when traded on future data.
The major disadvantage is that it is rather static, which will alter its performance with the volatility of the market. If the volatility is higher than average,
the system will have you stopped out with a loss more often than necessary, while
at the same time taking profits too soon, given the potential of the move as induced
by the increased volatility. If the volatility is lower than average, the profits will be
smaller than normal and more trades will be stopped out by the time-based stops.
To come to grips with the volatility changes over time, another way to calculate where to place the stops and exits is to use the average true range method.
Using this method, you always let the trade move with or against you with a prespecified number of true ranges. Because the true ranges will vary in size with
the volatility of the market, so will the distance between the entry price and the
exit points.
The major disadvantage with this method is that it needs historical data for the
true-range calculations, which complicates the system and makes it less robust. You
can work around this by setting the lookback period for the true range equal to either
the lookback period for the rest of the indicator or pattern, or to the maximum
allowed trade length. Personally, I prefer to go with the maximum allowed trade
length, and then test the trade length and the lookback period for the true range
simultaneously. As already mentioned, the maximum allowed trade length shouldn’t
differ that much from the lookback period for the indicator or pattern, anyway.
The best way to find the most optimal input-variable combinations is to analyze them using a surface chart, in which the color of the chart indicates the value
of the output. Once you’ve learned to interpret the information in a surface chart,
284
it becomes a breeze to find the values for the input variables that suit you and the
system best. Usually I test the system for three input variables at a time.
For example, for this book I tested the stop-loss and profit target distances
together with the maximum allowed trade length. I then compared the variables
two at a time, disregarding the third variable for the moment. In this way, I got 10
different test runs per variable combination and market tested. When looking at the
surface chart, I always try to come up with the variable combination that seems to
work best on average, over all test runs and markets tested.
An alternative way is to test for only two variables at a time and substitute
for the third variable a random-number generator that will produce a unique
sequence of trades each time you run the system through the market. The expert
exits system was developed this way for the June 2002 issue of Active Trader magazine. Be forewarned, however, that this method is very time consuming.
Using surface charts to examine several different stop and exit levels for five
of our systems, it turned out that the average true range concept worked best for
most systems. Interestingly, however, the percentage concept, which worked best
for the most short-term systems, also happened to work the best on both sides of
the market (both long and short trades).
The testing was done on both sides of the market for all systems tested,
although in the end we would only apply it to the long side. Similarly, the exits
were applied to all systems before the relative strength filters were added. We did
this because I believe that the more market conditions and circumstances that are
allowed to influence the final parameter setting, the more robust and reliable the
system will be when traded on future data.
Another way might have been first to apply the filters and then test only the
side of the markets that would be traded. This would probably have boosted the
profits considerably on the historical data, as the system would have been more
curve fitted to those exact conditions. The drawback would have been that the system would have been less robust and reliable for real-life trading in the future,
where everything still can happen.
While testing the stops and exits, we found several examples of how changing from a stop loss to a profit target resulted in completely different characteristics for a system. This is because a system often produces a series of entry signals
that might or might not result in a trade, depending on if we’re in a trade already
or not. Altering the way we exit the market also alters which signals will be available to enter on, which in turn will alter the most optimal exit levels and trade
lengths, and so on. These differences were further exaggerated when adding the
three systems saved for filtering, in Chapter 21.
The research in Chapter 21 also revealed that using a relative-strength filter
doesn’t necessarily add to the bottom line and the robustness of the combined
strategy. We identified several reasons. One of these reasons was that trading the
stock that seems to be the strongest both in the intermediate-term and short-term
CHAPTER 23
285
isn’t necessarily a good idea. Instead, it could be a better idea to trade the weakest
stock in a group of stocks as long as the general trend is in the direction of the
anticipated trade. The reason behind this logic is that the weakest stock is more
prone to an explosive move in the direction of the anticipated trade, to catch up
with the others.
We ended Part 3 by discussing an additional research method to gain further
confidence in the system. This method took all the trades produced by a system
and scrambled them around, before it put together several random trading
sequences, with new trading sequences made up of the historical trades. Using this
method, we examined a system for its consistency and likelihood for producing
profitable trading sequences in the future, given that the profits and losses remain
within the statistical confines identified by the historical testing, but with the actual order between the trades unknown.
PART
FOUR
Money Management
I
ronically, chances are that the less sure a trader is that the next trade will be a
winner, the better the trading strategy or the system. It sounds strange, but there
are two ways to think about this paradox so that it makes sense.
One way is to assume that the markets are as close to random as they possibly can be. Therefore, a strategy that works in a close-to-random environment
needs to be robust enough to maximize the potential of any nonrandom market
behavior when it appears, while still keeping you in the game when the market is
random. In other words, the best you can hope for is a strategy that can turn a profit under the worst of long-term circumstances (randomness).
Hence, most trades signaled by a system, whether they turn out to be winners
or losers, are because of random market moves; only a few trades, scattered among
all the signaled trades, are actually because of the type of nonrandomness the system tries to catch. The trick is to make the most of the latter category of trades while
breaking even or just barely producing a profit on all others. Unfortunately, however, there is no way to distinguish one type of trade from the other beforehand.
The second way is to look at the system as a tool with which we can soak up
and make use of the information the market gives us. If we were only trading on
random noise, the trades and the result would be random. If we were trading on
sure deterministic facts, the outcome of all trades would be certain. When we
make use of the information the market gives us, we’re taking the information
from the market and planting it into the system or trading model. The more information we take from the market, the less information is left to make use of, up
until the point there is only random market noise left. The more random noise is
left in relation to unused information, the closer to random the strategy will
behave, which ties back to our first way of thinking.
288
PART 4 Money Management
Traders instinctively want to avoid randomness, but this should not be the
case. Say you have discovered that your trading system, on average, produces two
winners for every three trades. This may be good news, but it does not mean the
strategy will always produce two winners followed by one loser, followed by two
winners, and so on.
To think that the strategy will follow a distinct pattern of wins and losses is
dangerous, because this assumption may cause you to risk too much on a losing
trade and not enough on a winning trade, when the pattern that you thought existed breaks down. Therefore, the more difficult it is to predict the outcomes of two
or more consecutive trades, the better the system will perform, because it will not
be based on potentially erroneous assumptions about the outcomes of any particular trades.
Following these lines of thinking, you can decrease your dependence on luck
by not only making sure your strategy is highly likely to produce winners (i.e., do
a good job of profiting from those rare nonrandom market moves and situations
that the system is designed to catch), but also, strange as it might sound, by making sure you still can’t predict the outcome of the next trade.
When it comes to the reliance on luck, both profitable and unprofitable
traders can be divided into smaller subgroups: those who are skilled and those who
are just plain lucky. If you truly care about your trading results, you need to know
how much of your profits depend on pure luck. Certainly, every active trader is
lucky to a certain extent, because the truth is there’s always a chance—however
slim—that the market will blow you out completely.
The trick is to make the likelihood for this as small as possible by keeping
your skill–luck ratio as large as possible. If you’ve managed to make a good living from trading, how do you know you couldn’t have done even better with a little more knowledge or skill? Or, if you currently are in a losing streak, is it your
high skill level that keeps you from losing even bigger during this dry spell, or just
dumb luck that is keeping you down?
CHAPTER
24
The Kelly Formula
A
dhering to your stops and exit signals is of paramount importance in becoming
a skillful trader. If for nothing else, even though you can’t make sure of the outcome of the next trade, you can decide what the maximum loss will be if it turns
out to be a loser by always risking the same relative amount on each trade. The
word relative is used to indicate that the amount risked should be constant, relative to the available capital, so that when your account grows, you will risk more
in dollar terms to keep a constant risk per trade in percentage terms.
The amount risked should stay constant because if there is no way of knowing the outcome of the next trade, the best we can do is risk the same amount all
the time, on all the trades. To state that another way, if an obvious relationship
existed between the outcomes of all trades, you should vary the bet size based on
whether the next trade would likely be a winner or a loser. However, because we
already know that there is no such relationship between trades for a good system,
the best we can do is risk the same amount all the time.
Also, even if there were such an historical relationship in the past, you are
probably still better off risking the same amount for all trades, as this relationship
may or may not continue to exist in the future. If it doesn’t, you again run the risk
of risking too much at some times and too little at others, which not only will result
in a slower than optimal equity growth but also an increased likelihood of going
broke.
Therefore, much of the balance between skill and luck is captured in how you
determine the size of each trade. One way to enhance your performance in this
area is to use the Kelly formula, which calculates how much capital should be
risked on each trade. However, the Kelly formula is only applicable to strategies
289
290
where every winner is the same size and every loser is the same size—hardly the
case in actual trading. Therefore, it should only be used as an approximate value
that should not be exceeded in trading. The Kelly formula looks like this:
K W (1 W) / R
Where:
K Kelly value
W Historical winning percentage
R Historical average win–loss ratio
To begin using the formula, we need to collect some information. Suppose
your five most recent trades ended with a win of 5 percent, a loss of 2, a win of 3,
a win of 1, and a loss of 6, then:
The average value of your winning trades is 3 percent [(5 3 1) / 3].
The average value of your losing trades is 4 percent [(2 6) /2].
The average win–loss ratio is 0.75 (3 / 4).
The likelihood for a winning trade is 0.6 (3 / 5).
The likelihood for a losing trade is 0.4 (1 0.6).
With W equal to 0.6 and R equal to 0.75 (3 / 4), K equals 0.067 [0.6 (1 0.6) / 0.75]. Thus, to make the most of your ability to pick good entry and exit
points, in this particular case no more than 6.7 percent of your trading capital
should be risked on each trade.
Once you know how much of your total equity to risk, you also can calculate
how many shares or contracts to buy to take on that risk and how much of your
available equity you should put toward a particular trade. To do this, you will need
a predetermined stop loss per share or contract. For example, say you’re considering a stock that currently trades at $50, and its chart shows $46 to be a good stoploss point. If you currently have $100,000 of trading capital, here’s how to figure
how much you can trade:
Calculate the amount to risk as the Kelly value times the account size (0.067
* 100,000 $6,700). With a stop loss of 4 points, determine how many shares you
can buy as the amount to risk divided by the stop-loss distance (6,700 / 4 1,675).
Calculate the amount of your capital that needs to go towards this trade as the
stock price times the number of shares to buy (50 * 1,675 $83,759).
The larger K is, the more money you can put into one trade; the smaller K is,
the less money you should put into one trade. Also, the tighter the stop loss, the
more of your capital you need to put into one trade; the wider the stop loss, the
less capital you need to put into one trade. For example, if the stop loss were only
two points away from the entry, then the Kelly formula suggests you should buy
3,350 (6,700 / 3) shares for a total value of $167,500 (3,350 * 50), which you can-
CHAPTER 24
The Kelly Formula
291
not do because you only have a $100,000. Or, if the K value equals 0.03, the
amount to risk should be $3,000 (0.03 * 100,000), and the number of shares to buy
would be 750 (3,000 / 4), for a total value of $37,500 (750 * 50).
Therefore, the larger K is, the looser the stop loss should be, so that the suggested amount to trade won’t exceed the available capital, or your maximum allotted (relative) amount for one trade. The looser the stop loss, the larger K can be
without making you exceed your available capital. Again, the word relative is
within parentheses to indicate that the maximum allotted amount can vary with the
total equity. Another hallmark of a skillful trader is the ability to find the right balance between these two variables, so that he can be in the desired number of positions simultaneously.
In the first example, we can only be in one trade at a time, given the amount
of money we have at hand [Integer(100,000 / 83,759) 1]. In the second example, we can’t trade at all [Integer(100,000 / 167,500) 0]. In the third example,
we can be in two trades at a time [Integer(100,000 / 37,500) 2]. Obviously, as
short-term system traders, we would like to be in at least 10 to 20 trades simultaneously. Thus, the distance between the stop loss and the entry price must be very
large, and the more positions we want to be in simultaneously, or the less we want
to risk per trade, the larger this distance should be. We will learn how to deal with
this in a little while, given that we already have decided on where to place our
stops in Part 3.
However, even armed with the knowledge of the system’s K value, there is
no guarantee that we won’t be extremely unlucky in the future. Figure 24.1 shows
the results from 100 trade simulations using the winning and losing percentages
and average trade values we have worked with so far. The y-axis represents the
profit or loss (the starting balance was set to 100). A large number of these simulations end up as losing propositions, even though we’re risking 6.7 percent of
available equity with a 60 percent chance of success. However, where and when
these winning and losing trades happen, which is determined randomly, still can
determine the overall profitability.
In the case of Figure 24.1, the best run produces an average profit per trade
of $426, while the worst run produces an average loss of 96 cents per trade, with
25 percent of all test runs ending up in negative territory. The risk–reward ratio,
calculated as the average profit per trade produced by all 100 test runs divided by
the standard deviation of all average profits, comes out to 0.41 (28.6 / 69.8), which
is not particularly good. (As already discussed earlier, preferably this value should
be above one.)
Obviously, a strategy needs to be better than this to keep the bad-luck consequences to a minimum. Let’s see what happens if we increase the win–loss ratio in
Figure 24.1 from 0.75 to 0.8 (for example, by trading a strategy with an average
winner of 4 points and an average loser of 5 points), which also increases the K
value to 0.1. Figure 24.2 shows the outcome of 100 such simulations.
FIGURE
24.1
Kelly formula applied to 100 trades.
FIGURE
24.2
Kelly formula using increased win–loss ratio.
292
CHAPTER 24
FIGURE
The Kelly Formula
293
24.3
Spreadsheet data for Kelly formula in Figures 24.1 and 24.2.
These results look much better, with the best run producing an average profit per trade of $1,064,251, while the worst run produces an average loss of 97
cents per trade. Even in this case, however, a slight (4 percent) chance exists that
the strategy will end up in negative territory. The charts in Figures 24.1 and 24.2
were produced with a simple spreadsheet, of which you can see a small part in
Figure 24.3.
To recreate the spreadsheet in Figure 24.3, type in the following formulas
and values:
In cell D3: Type in the ratio between the average winner and average loser.
In cell E3: Type in the percentage of winning trades.
In cell F3: Type in the formula E3(1E3)/D3.
In cells B6 to CW6: Type in the value 100.
In cell B7: Type in the formula IF(RAND()<$E$3,1$B$3*$D$3,1
$B$3)*B6, and drag and fill it into all cells down to CW1006.
In cell B1008: Type in the formula (B1006100)/100, and drag and fill it
into all cells to CW1008.
In cell H3: Type in the formula MAX(B1008:CW1008).
In cell I3: Type in the formula MIN(B1008:CW1008).
In cell J3: Type in the formula AVERAGE(B1008:CW1008).
In cell K3: Type in the formula STDEV(B1008:CW1008).
In cell L3: Type in the formula J3/K3.
In cell M3: Type in the formula COUNTIF(B1008:CW1008,">0").
In cell B3: Type in the value in cell F3.
Ideally, the better a strategy is at picking tops and bottoms, the more you
should risk per trade. However, the more you risk per trade, the more you stand to
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lose when that inevitable series of bad trades strikes. And the higher the K, the
shorter that series of bad trades needs to be to wipe you out.
The previous examples also assume that what held true in the past also will
hold true in the future. Most likely, though, that will not be the case. Extrapolating
a little from Murphy’s Law, a strategy will most likely not work as well in the
future as it has in the past or during testing. Therefore, one should always trade at
a K value considerably lower than what is calculated as ideal to maximize the equity. Although this might mean a less-than-optimal equity growth, it also means a
higher likelihood of not being thrown out of the game. In other words, you’re
decreasing the role of luck—good and bad—in your trading.
For example, with the help of the spreadsheet you can try different K values
higher or lower than the one calculated. If you do, you will find that trading at a
K value higher than the calculated K might result in a few test runs producing
higher returns, but also that more test runs will end up with a loss. Similarly, trading at a K value lower than the calculated K will result in a slower equity growth
for most test runs, but also in more runs that are profitable.
In the extreme example, if you risk everything you have on each trade, it will
only take one loser to wipe you out completely. Even if you don’t risk everything
on each trade, a series of bad trades, where you’ve risked too much, can still force
you out of the game. On the other hand, being too conservative won’t make the most
out of a good trading strategy. Generally speaking, the relationships are as follows:
Risking too little on each trade results in small losses and shallow drawdowns,
but the equally small profits will keep you in the drawdowns for a long time and
the overall equity growth will be slow. When risking too much on each trade, the
losses will be large and the drawdowns deep, but the large winners will help you
get out of them rather quickly and the overall equity growth will be fast. The paradox is that the larger the drawdowns you allow, the faster the equity growth. But the
larger the drawdowns allowed, the larger the likelihood to go bust. Also, the larger
the drawdowns, the more erratic your equity curve, the riskier the trading in general terms, as measured by the risk–reward ratio. Thus, we need to balance the steepness of the equity curve with its smoothness so that the steeper the better and the
smoother the better. We do this by finding the proper amount to risk, which will
govern the size (both in magnitude and time) of the drawdowns. One way to do this
is to use the Kelly formula, and not trade past the calculated K value.
As already mentioned, the major flaw of the Kelly formula is that it assumes
two outcomes only—a winner of a certain magnitude and a loser of a certain magnitude. Trading, with its virtually infinite number of potential outcomes per trade,
is not such a simple game, however. The Kelly formula should, therefore, be used
only for initial research and experimentation. For a better approximation of the
optimal trade size, one should determine what is popularly known as the optimal
f, which requires a slightly more complex calculation.
CHAPTER
25
Fixed Fractional Trading
Because winners and losers obviously aren’t always the same size, we need to find
a formula that can account for varied trade outcomes. One such formula is the formula for optimal f, which was popularized by Ralph Vince in his book Portfolio
Management Formulas: Mathematical Trading Methods for the Futures, Options,
and Stock Markets (John Wiley & Sons, 1990). This formula is designed to maximize equity growth by making the outcome of each trade dependent on the amount
you are willing to risk in relation to the risk per share traded and the worst historical losing trade.
The formula works with compounded returns and the fixed fraction of your
capital to risk per trade that produces the highest compounded return, which Ralph
Vince named terminal wealth relative (TWR) or optimal f. Because the returns are
compounded, TWR is calculated by multiplying the percentage returns from each
individual trade, so that:
TWR = HPR1 * HPR2 * HPR3 * … * HPRi
Where:
TWR = Terminal wealth relative, expressed as the percentage compounded
return over a trading sequence.
HPRn = The holding period return for trade n, expressed as a percentage of
your total equity going into the trade.
That is, the HPRn is the percentage profit for trade n, for a given fraction (f)
risked per trade, with the same fraction for all trades within the same test run or
sequence of trades. Altering the fraction to risk of the available equity will produce
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different HPRs and consequently different TWRs for different test runs or trading
sequences. To calculate the HPRn, Ralph Vince suggested the following formula:
HPRn = 1 f * (Profitn / WCS)
Where:
f the fixed fraction of your capital to risk in all trades.
Profitn = The profit or loss from trade n in dollars on a constant-sharesinvested basis.
WCS = The historical worst-case scenario in dollars on a constant-sharesinvested basis (expressed as a positive number).
According to the terminology used by Ralph Vince, the value of f that produces the highest TWR is the called the optimal f. The best way to find optimal f
is to build a spreadsheet in which the results are dependent on f. In other words,
the spreadsheet should be designed so that typing in a new value for f changes the
values in all other cells. This is how a recommended risk level is determined for
the Trading Systems Lab in Active Trader magazine.
Figure 25.1 shows a small part of such a spreadsheet that allows you to test
either a random or an actual trading sequence of 100 trades. The result from each
trade is typed or imported into cells B13 to B112. If you use a random series just
FIGURE
25.1
Spreadsheet data used to calculate optimal f.
CHAPTER 25 Fixed Fractional Trading
297
to get a feel for how it works, you can change the largest winning and losing trades
allowed and the desired percentage of profitable trades, in cells G2 to G4. To create a similar spreadsheet for yourself, type in the following formulas:
In cell G2: Type in the value of your largest loser in percent (in this case
“2”).
In cell G3: Type in the value of your largest winner in percent (in this case
“6”).
In cell G2: Type in the desired percentage of winning trades (in this case
“32”).
In cells E11 to GW11: Type in the value for f in percent, in steps of 0.5 percents, starting with zero in cell E11, ending with 100 in cell GW11.
In cells E12: Type in the value “1,” and drag and fill it all the way to cell
GW12.
In cell C12 to C112: Type in a number series, in steps of one, starting with
zero in cell C12, ending with 100 in cell C112.
In cell B13: Type in the formula
IF(RANDBETWEEN(1,100)<G$4,RAND()*G$3,RAND()*G$2),
and drag and fill it into all cells down to B112. (This formula can be
replaced by typed-in or imported results from real trades.)
In cell E13: Type in the formula (1($B13/$G$2)*(E$11/100))*E12, and
drag and fill it into all cells to GW112.
In cell E113: Type in the formula IF(E112$G6,E11,0), and drag and fill
it all the way to cell GW113.
In cell G6: Type in the formula MAX(E112:GW112).
In cell G7: Type in the formula SUM(E113:GW113).
In cell G8: Type in the formula G6^(1/100).
In cell J6: Type in the formula (G6-1)*100.
In cell J8: Type in the formula (G8-1)*100.
Once this setup is created, you can recalculate the spreadsheet using random
numbers by pressing the F9 button, or calculate the TWRs corresponding to each
f, for a real or back-tested trading sequence. Figure 25.2 shows a chart for how
TWR relates to f for such a random run, with the maximum allowed largest winner and loser and percent profitable trades according to the values in Figure 25.1.
As you can see from Figures 25.1 and 25.2, the optimal f for this random series
equals 10.5 percent, which means that to achieve the highest possible TWR, we
should risk exactly 10.5 percent of our available equity in each trade. If we risk
less than that, we won’t optimize our profit potential, as will a risk of more than
10.5 percent. And if we risk as much as 25 percent of our available capital per
trade, we won’t make any money at all, but start losing it instead.
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FIGURE
25.2
TWR relative to f in a random trading run.
Furthermore, even though we might not risk as much as 25 percent per trade,
which assures that we will go broke eventually, we still run a larger risk of going
broke if we risk slightly more than the optimal f, compared to risking slightly less
than the optimal f. The more we risk, the larger the price swings—both good and
bad—and the larger the swings, the greater the risk that one of the swings to come
will be too large to handle. Figure 25.3 shows how the equity varies with different
fs. As you can see, the lower the f, the smoother the equity curve and the smaller
the drawdowns, but also the slower the equity growth. On the other hand, the larger the f, the faster the equity growth—up to a point—but also the deeper the drawdowns and the corresponding time it will take to recover from them.
A simple example can further explain the formulas for TWR and HPR.
Assume that we already found optimal f to be 0.05, which means that we should
risk 5 percent of our equity per trade. Suppose also that our worst historical loser
was $10,000 and that we have two trades that each produced a profit of $5,000 on
a constant-shares basis. In that case, each HPR comes out to 1.025 [1 0.05 *
(5,000 / 10,000)] and the TWR comes out to 1.0506, which equals a total return of
5.06 percent on total equity going into the trading sequence.
FIGURE
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25.3
Equity versus optimal f.
Applying this kind of money management means we always make use
of our winnings from the previous trade, which is why all HPRs are multiplied with each other when calculating the TWR and why two trades that produce a profit of 2.5 percent each produce a total profit of slightly more than
5 percent.
For example, if your initial capital is $100,000 and you make 2.5 percent per
trade on two consecutive trades, your total profit will be $5,063. The $2,500 profit on the first trade would be added to your capital, and you’d make $2,563 on the
second trade (102,500 * 0.025).
Two main points of criticism of this version of the optimal f formula arise.
First, the better the underlying buy and sell decisions, the higher the optimal f. The
higher the optimal f, the more you stand to lose in a losing trade, simply because
the formula tells you to risk more. Some would say that this makes fixed fractional trading too risky for any practical purposes.
Second, to keep the fractional risk amount constant, the dollar amount risked
will vary with the account size. For large accounts, this can translate into enormous and very uncomfortable amounts of dollars risked. For small accounts, the
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relatively slow equity growth in dollar terms might not be enough to increase the
number of shares traded.
However, the way I see it, the critics overlook two important points. First,
nothing forces anyone to trade the exact optimal f. The important thing is to not
take any unnecessary risk by trading above it. Also, never forget that the optimal f
value is based on historical or back-tested trades. As already stated, chances are
Murphy’s Law will make sure that the system will not work as well in the future
as it has in the past—at least not initially—which means that the true f for that
period of trading will be lower than the historical f. Therefore, it’s better to be safe
than sorry and trade at an f considerably lower than the optimal f derived from historical data. To do that, you need to know where f is in the first place.
To trade below the historical optimal f, you need to decide how much below
you must go to achieve a suitable risk–reward relationship. Remember, the less
you risk, the less you will lose and the smaller the drawdowns will be. For example, it is fully possible to calculate an f that aims to find an equity curve that is as
smooth as possible in relation to the equity growth, or one that simply aims to minimize drawdowns and/or flat times, or….
Second, in Ralph Vince’s original version of the formula, f depends on the
worst historical loser. We use the largest historical loser in the formula for the HPR
because we implicitly assume that one reason why we’re trading this system in the
first place is that its largest historical loser is within the limits for what we can tolerate given the system’s overall profit potential, but also because the loss has
already happened (whether for real or during testing), which, because of its size,
makes it less likely to happen again.
Note, however, that the “better” the system, the higher the optimal f will be,
because the better the system, the more we should be able to risk per trade to make
the most out of the system by maximizing its profit-generating potentials.
However, if we ever were to encounter a loss of the same size as the worst historical loser, so that Profitn equals WCS, then the HPR for that trade also will equal
f, according to the formula HPRn 1 f. Thus, the better the system, or the higher its profit-generating potential, and the higher the f, the more you stand to lose
on one single trade, should the system once again experience a loser of the same
magnitude as the worst historical loser.
I know of traders who claim to have systems good enough that they trade
them with an f of 0.20, meaning they’re risking 20 percent of their capital in any
one trade. Is this a wise thing to do, no matter how good the system is? No, of
course not. Risking as much as 20 percent per trade means that it will only take
three losing trades in a row to deplete the trading capital by close to 50 percent.
That is, after three trades, losing 20 percent of your capital in each trade, you’d be
in a 50 percent drawdown. To get back to where you started you would need to
increase your current capital by 100 percent, for which you’d need at least four 20
percent winners in a row—how likely is that?
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No serious trader should ever risk more than a few percent of his total capital per trade. Trading with such a high f as 20 percent will severely reduce your
staying power when you hit a streak of bad trades (and in this case you only need
three to reach a drawdown of 50 percent), which will unarguably happen at some
point.
There also are plenty of other ways to calculate an f that is not based on the
worst historical loser. Personally, I prefer to substitute for the worst historical loser
whatever I am prepared to lose per share for that particular trade. This is easily
done by substituting the WCS with the stop-loss level for that particular trade and
for all trades and do all the calculations on a one-share basis. In this case, the
worst-case scenario will be based on what you’re willing to tolerate for this very
trade, instead of what you were willing to tolerate in the past while hoping that
experience won’t repeat itself.
For example, assume again we already found the optimal f to be 2 percent.
Suppose also that we are willing to risk $2 per share on a $100 stock and that the
trade ended with a profit per share of $5. Then, the HPR for that trade will be 1.05
[1 0.02 * (5 / 2)], or 5 percent of available equity going into the trade. Now, suppose a second trade on a different stock, priced at $50 and with a stop loss of
$1.25, ends up with a profit of $2. Then the HPR for that trade will be 1.032 [1 0.02 * (2 / 1.25)], or 3.2 percent of available equity going into the trade. The TWR
for these two trades will be 1.0836 (1.05 * 1.032), or 8.36 percent of the available
equity going into the trades.
It is also a good thing to substitute for the WCS an individual stop loss for
each trade because the stop loss is not a once-in-a-lifetime (hopefully) terrifying
experience, but a rather reasonable amount that you are prepared to encounter frequently. This is good news, because if you take a look at the formula for the HPR
again, you will see that the smaller the WCS, the larger the factor Profitn / WCS.
Thus, the f can be lowered to produce the same HPR. In other words, the less we
are willing to risk per share traded, by lowering the value for the WCS to an
amount more suitable to each specific trade, the less we need to risk of account
equity to achieve the same HPR and, ultimately, TWR.
Using a variable stop loss while risking the same relative amount of your
capital for each trade, it still is simple to calculate the number of shares to trade
and the exact amount of capital needed for each trade. First, after figuring out the
percentage of capital you’re willing to risk, determine the stop loss for your next
trade. For example, if you go long at 100 and your stop loss is placed at 96, you
are willing to lose four points per share. Next, multiply your account balance
entering the trade with the f value you have decided on. For example, if your
account balance is $100,000 and your f is 0.02 (2 percent), you’re willing to lose
$2,000 per trade (100,000 * 0.02).
Then divide the total amount you’re willing to risk per trade by the amount
you are willing to risk per share to arrive at how many shares you need to buy. In
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this case, you’re willing to risk $2,000, and your risk per share is four points, so
you need to buy 500 shares to take on a total risk of $2,000 (2,000 / 4). Finally, if
the stock is priced at $100, the entire trade will tie up $50,000 of your capital (100
* 500). These calculations are essentially the same as those we just did in Chapter
24, when discussing the Kelly formula. More formally, the formulas can be stated
as follows:
ST (AC * f) / SL
and
MT ST * EP
Where:
ST Shares to trade
AC Available capital
f Fraction of capital to risk
SL Stop loss, distance transformed to points from percentages between
the entry price and stop-loss level
MT Money tied up in trade
EP Entry price of stock
I’m being redundant here, but I want you to get a firm understanding of this,
and as the saying goes, repetition is the mother of all knowledge. On that note, I
once again would like to point out that the more you are willing to risk per share
and the lower the f, the less money you tie up in the trade. The trick, then, is to balance the f and the SL so that you can be in as many positions as you desire at the
same time. In the previous example, with the account balance at $100,000 and
with the trade tying up $50,000, you can only be in two similar positions at the
same time [Integer(100,000 / 50,000)].
However, if you lower the f to 1 percent and increase the SL to six points, a
single position will tie up $16,600 [100,000 * 0.01 / 6 * 100], and you can be in
six similar positions at the same time [Integer(100,000 / 16,600)]. The chore is to
find a trading strategy that makes it possible to be in the desired number of positions given your account equity. The difficulty is, however, that to increase the
number of possible positions to be in at any one time, the stop loss needs to be
placed further away from the entry price than what might make sense for a shortterm strategy.
In the last example, the stop loss was placed 6 percent away from the entry.
For a decent risk–reward relationship going into the trade, the profit potential,
therefore, needs to be at least 12 percent, for an initial risk–reward relationship
of 2:1. This isn’t all that realistic for a short-term trading strategy. We will learn
how to work around this dilemma soon, but first we need to back up to the for-
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mula for calculating the TWR, to gain a little better understanding of how the
entire process works.
Just as one can calculate an arithmetic average for any data series, so too can
we calculate an average value representing all the HPRs making up the TWR.
Because we are working with multiplication and compounded returns, however,
this average must be a geometric average. For example, to calculate the average
arithmetic return from three profitable trades of 3, 5, and 7 percent, respectively,
simply add them up and divide by the number of trades. In this case, the arithmetic
average equals 5 percent [(3 5 7) / 3]. Without compounding the returns, the
total return can be calculated either as (3 5 7 15), or as (3 * 5 15). With
an initial account equity of, for example, $100,000, the resulting balance is
$115,000 [100,000 * (1 15 / 100)].
Using compounding, we need to use multiplication instead of addition.
Therefore, the three different returns need to be expressed as 1.03 (1 3 / 100),
1.05, and 1.07. Had one of the returns been negative because of a losing trade, the
plus sign would have been replaced by a minus sign, so that, for example a 3 percent losing trade would have been stated as 0.97 (1 3 / 100). Multiplying these
values would result in a compounded return of 1.1572 (1.03 * 1.05 * 1.07), which
would result in a compounded resulting balance over the three trades of $115,720
(100,000 * 1.1572). Now, to calculate the average return over the three trades, we
need to calculate the geometric mean (GM), which, because we’re dealing with
multiplications will be 1.0499 (1.1572(1/3)), or 4.99 percent [(1.0499 1) / 100].
A more general relationship between TWR, HPR, and GM can be expressed as:
TWR GMN HPR1 * HPR2 * HPR3 * … * HPRi
So that:
GM (HPR1 * HPR2 * HPR3 * … * HPRi)(1/N) TWR(1/N)
Where:
GM The geometric mean
N Number of trades
The formulas might look a little advanced, but don’t forget that the entire
process is akin to calculating the regular arithmetic average profit per trade,
expressed in percentages. Now, the next step also might look a little advanced, but
it really isn’t. Let’s just settle for the fact that there is an alternative way to calculate GM that incorporates the arithmetic average profit, which we calculated at 5
percent in the previous example. This formula looks like this:
GM = (APM2 – SD2)(1/2)
Where:
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APM The average profit multiplier, calculated as the average percentage
profit per trade divided by 100, plus one, which, using the numbers from
the example above, comes out to 1.05 (1 5 / 100).
SD Standard deviation of all trades, measured in percentage terms, so that
for a standard deviation of 25 percent, SD equals 0.25 (25 / 100).
Given these formulas, the TWR also can be expressed as:
TWR GMN (APM2 SD2)(1/2)N (APM2 SD2)(N/2)
This formula also might seem a little complicated at first glance, but the
interpretation is quite simple. To end up with a positive TWR, all we need to do is
keep APM larger than SD. This should explain all the hard work we went through
earlier to lead to this part on money management. This is why we want the system
to operate with specific stop loss, profit target levels, and trade lengths, and also
to work on as many markets or market situations as possible. Because when it
does, we know we’ve done everything we can, not only to make sure that APM is
as large as possible in relation to SD, but also to make sure that this relationship
will hold up in the future.
If we can achieve this, the end result for TWR will only be a function of f (the
fraction of available equity to risk) and N (the total number of trades). The more
trades, the greater TWR will be. This also explains our obsession with testing the
system on as many markets as possible and making the trades as short term and
similar as possible, because to maximize TWR we need plenty of trades, and to
maximize N we need markets to trade. With a large number of markets to trade,
producing a large number of trades, we can tailor TWR to our needs and expectations, by experimenting with different fs, according to the formula for HPR.
CHAPTER
26
Dynamic Ratio Money Management
T
ailoring optimal f, TWR, and HPR to our goals brings us back to the importance
of finding the right balance between f and the amount to risk per share, so that we
can make as many trades as possible, in as many markets as possible, wasting as
little time as possible. Frequent short-term trading usually means a rather low
average profit per trade and the use of tight stop losses that make sense in relation
to the estimated and desired average trade length. The drawback is that the shorter-term the system, the tighter the stops on a one-share basis need to be, and the
tighter the stops, the fewer trades we can be in simultaneously for any given f. The
less we risk per share, the more shares we need to buy to reach f, and the more
shares we need to buy, the more money we need to tie up in the trade.
For example, say that our system calls for a stop loss that is placed only 2
percent away from the entry point, on average. For a $100 stock, this means two
points (100 * 0.02). Further, assume that we don’t want to risk more than 1 percent of our available capital per trade. With $100,000 in available capital, we therefore should buy 500 shares of the $100 stock [(100,000 * 0.01) / 2], which will tie
up $50,000 of our capital (500 * 100). As a consequence, we can only be in two
similar trades simultaneously [Integer(100,000 / 50,000)].
Note that it doesn’t matter how much money we have or how much the stock
costs. Given a 2 percent stop loss and an f of 1 percent, we can only be in two
trades simultaneously, no matter the values of the other variables. For example, if
we substitute a $10 stock for a $100 stock and increase the available capital to
$1,000,000, at first glance it seems as if we should be able to be in plenty more
positions at one time. But because the stop loss will be only 20 cents away from
the entry price (10 * 0.02), and the number of shares we need to buy will be 50,000
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[(1,000,000 * 0.01) / 0.2], for a total amount of $500,000 (50,000 * 10), once
again this only allows for two positions [Integer(1,000,000 / 500,000)].
To work around this, separate the stop loss (SL) from what I call the money
management point (MMP). So far, we’ve assumed SL to be equal to MMP, which
implicitly has resulted in the following formula:
ST (AC * f) / SL (AC * f) / MMP
Where:
MMP Money management point in distance from the entry price, to calculate the number of shares to trade
However, by separating the two and placing MMP further away from the
entry price, we can lower ST and also MT, which makes it possible to be in more
positions at the same time. As a consequence of this, the f used in the formula ST
(AC * f) / MMP won’t represent the true fraction risked of the available equity,
but rather just a fictive fraction used to calculate ST and MT. Therefore, from now
on, let’s call the f in the formula ST (AC * f) / MMP for ffict, so that the formula instead reads:
ST (AC * ffict) / MMP
Where:
ffict Fictive fraction of capital to risk to calculate the number of shares to
trade
Because the account equity and the price of the stocks have nothing to do
with how many positions we can be in using a DRMM regimen, the formulas for
the average number of simultaneously open positions and the average percentage
amount of equity tied up in one position can be simplified to the following two
formulas, respectively:
MMP / ffict
and
ffict / MMP
Figures 26.1 and 26.2 show how these formulas can be used to put together
tables that will help us get a feel for how to balance MMP and ffict against each
other, so that we can trade as many positions simultaneously as we desire. For
example, for an ffict of 2 percent, Figure 26.1 shows that we need the MMP to be
at least 20 percent away from the entry price so that we can be in 10 positions
simultaneously. Figure 26.2, in turn, shows that we then will tie up 10 percent of
our equity in each position, on average. To create the tables, simply type in the values for MMP and ffict manually in column C and row 4, respectively, then:
FIGURE
26.1
The equation MMP/ffict.
FIGURE
26.2
The equation ffict/MMP.
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308
In cell D5: Type in the formula INT($C5/D$4), and drag and fill it into all
cells to S29.
In cell D34: Type in the formula IF(D5>0,1/D5,0)*100, and drag and fill it
into all cells to S58.
Note that the term “on average” is used, because just as the stop loss can fluctuate with the average true range, so can the MMP. The next trick, then, is to figure out approximately how far it is to a certain percentage distance, on average and
over the long term. First, we need to figure out what our true f will be, given a ffict,
a MMP, and a SL. If ffict and f are expressed as fractions (i.e., the percentage value
divided by 100), the formula is:
f ffict * (SL / MMP)
For example, if the MMP is placed 10 percent away from the entry price, and
we calculate the number of shares and the amount of money to tie up in the trade
according to an ffict of 4 percent, then, if the trade hits the stop loss at, say 3 percent away from the entry price, the true f of the available equity risked and lost on
the trade will be 1.2 percent [(4 / 100) * (3 / 10) * 100]. However, just as the losses actually will be smaller than the fictive risk we take, so will the profits. From
the formula above, we can see that the larger the difference between SL and MMP,
the smaller the true profits and losses will be for any given ffict. This is also something we need to balance to find the desired smoothness and growth rate of the
equity curve.
The questions that now remain to be answered are how many positions, on
average, do we want to be in simultaneously, and how many markets do we need
to track for trading opportunities to make that possible? The first question you
must answer subjectively, with the answer based on your trading experience and
desire for action, but let’s say that we would like to be in 10 positions simultaneously, on average.
Having decided on an average of 10 positions, we can go back to the table in
Figure 26.1, where we can see that if we place the MMP 10 percent away from the
entry price, on average, then we should set ffict to no higher than 1 percent.
Likewise, if we set ffict to 2 percent, then we can place the MMP 20 percent away
from the entry price, on average. Because we know from experience that we most
likely won’t set ffict any higher than 2 percent or any lower than 1 percent, let’s try
to set MMP approximately 15 percent away from the entry price, so that the
desired amount of open positions corresponds to a ffict of 1.5 percent. Many times,
we might be in fewer positions and at times we might be in a few more. It all
depends on the volatility of the market, which will alter the magnitude of the true
range. On average, however, we will be in 10 positions simultaneously.
With this decision made, we need to go back to the normalized performance
summary for the system, which we made extensive use of in Parts 2 and 3, and fig-
CHAPTER 26
309
ure out how much time each stock spends in a trade. For example, if each stock
examined spends an average of 25 percent of its time in a trade, theoretically we
then could spend 100 percent of the time in the market, in one stock or another, by
moving in and out of four stocks, if we always could exit one trade and immediately enter into a new trade.
But because no four stocks will move in perfect synchronization like this, we
might need to track another one or two stocks, to always be prepared to take a
trade. In doing so, however, there also might be situations when we can’t take a
trade because we might be fully invested already. Better to miss a trade because
we’re fully invested than to miss a profit opportunity because we’re not tracking
enough stocks.
Likewise, if the average time spent in the market for a specific stock is 15
percent, then we need six to seven perfectly synchronized stocks to be in the market 100 percent of the time. Adding one or two stocks for a little overlap, we might
need to track seven to eight stocks, so that we can have at least one open position
at any time.
Given that most (short-term) strategies spend around 15 to 20 percent in the
market per stock traded, and given that we will try to be in no more than 10 stocks,
on average, simultaneously, this means that we need to track 60 to 70 stocks. The
more systems we trade, the fewer the markets we need to track, because each system adds to the time spent in the market for any individual stock. (This gives rise
to two interesting questions we will leave unanswered in this book, but that are
nonetheless important to contemplate: First, are we better off diversifying via the
number of markets monitored or the number of systems traded? Second, should
the systems themselves be looked upon as separate asset classes?)
One question we will answer is how wide, in percentage terms, is one average
true range? Knowing this, we will know how many average true ranges away from
the entry price we should place the MMP, so that it will be 15 percent on average.
The answer is that, at the time of writing, one average true range is approximately
4 percent wide in relation to the close of the same bar. This number is calculated
over the last 2,500 days on the 58 stocks used to research this book. To place the
MMP 15 percent away from the entry price, on average, we therefore need approximately four true ranges, rounded to the nearest whole numbers.
Incidentally, all this makes perfect sense from a risk management point of
view. The logic is as follows: The lower the volatility, the closer SL and MMP will
be to the entry price, and the more shares and money we dare tie up in any individual trade, because the volatility and risk is low. Also, because the risk is low,
we don’t need to diversify as much, which we can’t do anyway because each trade
ties up more money than normal. On the other hand, if the volatility and the risk
is higher than normal, the further away SL and MMP are from the entry price.
Thus, we avoid getting stopped out too frequently, while at the same time the fewer
shares and less money we dare tie up in any one position. Also, because the risk is
310
higher, we would like to diversify more, which we can do because of the smaller
amount of money tied up in each position.
Note that using DRMM does not mean that we let the volatility of the market alter the amount risked. Instead, it means that we let it alter the way we risk it,
by altering the ratio between the total amount risked and the risk per share—by
altering the ratio between the stop loss and money management point and the entry
price. In the end, this also alters the ratio between the number of possible open
positions and the number of stocks tracked. Because these ratios constantly change
with the volatility of all markets tracked and the f we have decided to use, to
achieve our desired risk–reward ratio when it comes to the equity growth, I have
dubbed this money management method dynamic ratio money management, or
DRMM, for short.
BUILDING A SAMPLE SPREADSHEET
We now know how to set a stop loss and a money management point, calculate the
number of shares to trade and the total amount committed, and how much we stand
to win or lose on the trade, all depending on the fictional f we decide to apply to
the system. But how to decide on the fictional f? And how to do that for all open
trades on several different markets, traded with several different systems, running
simultaneously? Let’s take this process step-by-step and at the same time construct
an Excel spreadsheet that will do the work for us:
The first step is to type down the development of each trade, on a one-share
basis, as in Figure 26.3. Figure 26.3 shows a few trades for Market 2, recorded in
columns L to P. In this case, the spreadsheet is for three markets, with the same
data for Markets 1 and 3 recorded in columns B to F and V to Z, respectively.
Figure 26.3 shows that the first trade for this market started on row 11 and ended
on row 14. Each row represents one day of trading. The actual dates for this trade
aren’t shown, but are recorded in the A column (hidden from view in Figure 26.3).
Figure 26.3 shows that the entry price for the first trade was $32 (column L)
and, at the time for the entry, the MMP was set to 2 points (columns M) and the
stop loss to 0.75 points (column N). These values remain the same for as long as
the trade remains open at the end of that day’s trading, going into the next day.
Consequently, as long as the trade remains open at the end of the day, the open
profit and loss is recorded in column O. At the end of the last day of the trade (row
14), only the closed-out profit or loss is recorded (column P).
This particular trade lasts for two full days, plus one day when the entry
took place (which could have happened anytime during the day), plus one day
when the exit took place (which also could have happened anytime during the
day). Here it lasted four days, but different software calculates the number of days
differently. TradeStation, for example, doesn’t count the day of the entry as a day
in a trade.
CHAPTER 26
FIGURE
311
26.3
Trades to be tracked for the Excel spreadsheet.
Figure 26.4 shows the input variables we can alter to alter the calculated
results in Figure 26.5. By altering the fictive risk in cell C3, all the values in Figure
26.5 will change as a result of all the changes that will take place for each day or
row, for all markets and trades recorded in the spreadsheet. More specifically, by
altering the value for the fictive risk in cell C3, we alter the amount of money
allowed to be risked in each trade, given the total amount of money available as a
result of all the days of trading leading up to each new trading day.
Thus, although the data recorded on a one-share basis always will look the
same, the actual result of that trade will change with the value in cell C3, and how
that value not only changes the amount of capital allotted to a specific trade, but
to all other trades as well.
312
FIGURE
26.4
Input variables to be altered.
FIGURE
26.5
Results of varied input variables.
The trick is to test your system with several different fictive risk levels and
decide on one that makes sense to you. As already mentioned, the optimal f, as
defined by Ralph Vince, only looks at the fastest historical equity growth, which
could make the system very risky to trade on future unseen data. Other ways to
select f could be to go for the f generating the highest profit factor, the highest
risk–reward ratio, the smallest average drawdown, the shortest flat time, the most
profitable time periods (such as weeks or months), or the best compromise based
on all this information. Remember never to trade a system on its historical optimal
f for the fastest equity growth, as that most likely will be too risky.
Figure 26.5 shows the evaluation variables we will learn to calculate with this
spreadsheet. These are far from all the variables needed, but it would be impossible for me to describe them all. Figures 27.2 and 27.3 show you a more professional set of evaluation variables, which are derived with the help of the spreadsheet I use to build the systems for Active Trader magazine. But for now, let’s stick
to Figure 26.5 and describe each evaluation variable one at a time.
The ending equity in cell H2 is the value of our portfolio at the end of the
testing period, including the value of any open positions, based on the price of the
stock, the number of shares purchased, and the profit or loss of the open position.
The total return in cell H3 is the percentage difference between the starting
balance in cell C2 and the ending equity in cell H2. In this case, we only examine
CHAPTER 26
FIGURE
313
26.6
Total number of shares, amount risked, and profits for each trade.
short period of trades. If the testing period stretches out for several years, you
could also calculate the average return for various time periods, such as years,
months, and quarters.
The value in cell H4 shows the total number of trades taken during the test
period. Note that this number can alter depending on the value in cell C3. The
more we risk per trade, the more we also need to tie up in that trade, and if we tie
up too much, there won’t be any money left for any succeeding trades as long as
the current trades remain open. Thus, the percentage of winning trades in cell H5
can also change because of the same reason.
The value for the maximum drawdown in cell J2 will most likely increase the
higher the value in cell C3. Note, however, that where and when the maximum
314
FIGURE
26.7
A running total portfolio summary.
drawdown took place doesn’t have to remain the same, but can change with the fictive f. In Figure 27.2, I also calculate the average drawdown, which can function as
an input to the drawdown freak-occurrence calculation we learned about in Part 1.
Remember, the drawdown is not a core system characteristic, but a function of other
system characteristics, and a large drawdown isn’t necessarily a bad thing.
There is no saying how the maximum flat time will change with changes in
the fictive f. Sometimes a large f creates deep drawdowns that take a long time and
many trades to get out of; at other times a large f increases the value of the winning trades leading out of a drawdown, thus shortening the time it takes to get out.
As with the drawdown, the time covering the longest flat time also can change
with the f.
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315
For this spreadsheet, the risk–reward ratio is calculated as the average daily
equity growth in percent, divided by the standard deviations of the daily percentage returns. These numbers are calculated for the total value of the portfolio,
incorporating the returns for both open and closed out trades. In Figure 27.2, this
value is referred to as the Sharpe ratio. In a more professional spreadsheet, this
value can be calculated on the monthly and yearly period returns, which also takes
other income streams, such as the interest earned on the money in the account, into
consideration. The higher this number, the faster the equity growth in relation to
the fluctuations in the returns.
The profit factor is the gross profit divided by the gross loss from all trades
actually executed. This number will change with f for two reasons. First, the size
of a specific profit or a loss will depend on the amount invested in that trade,
which depends on the outcome of all trades preceding it. Second, as already mentioned, if the f is too high, some trades might be skipped completely.
The formulas for this specific spreadsheet and Figure 26.5 read as follows:
To calculate the ending equity, in cell H2 type: =AG128, where cell AG128
denotes the ending equity for this trading sequence. Remember to change row references with the length of the test period and the column reference with the number of markets.
To calculate the total return, in cell H3 type: (H2C2)/C2, where cell C2
denotes the initial balance (see Figure 26.4).
To calculate the number of trades, in cell H4 type:
COUNTIF(K11:K128,"<>0")COUNTIF(U11:U128,"<>0")
COUNTIF(AE11:AE128,"<>0"), where columns K, U, and AE denote
the results from each trade in Markets 1, 2, and 3, respectively. (See sample
trades for Market 2 in Figure 26.6, other markets not shown.)
To calculate the percentage of winning trades, in cell H5 type:
(COUNTIF(K11:K128,">0")COUNTIF(U11:U128,">0")
COUNTIF(AE11:AE128,”>0”))/H4
To calculate the largest drawdown, in cell J2 type: MIN(AJ10:AJ128),
where column AJ denotes the daily drawdown number for the portfolio (see
Figure 26.7).
To calculate the longest flat time, in cell J3 type: MAX(AK10:AK128),
where column AK denotes the number of days since the last equity high
(see Figure 26.7).
To calculate the risk–reward ratio based on the daily fluctuations in the equity, in cell J4 type: AVERAGE(AL11:AL128)/STDEV(AL11:AL128),
where columns AL denotes the daily equity fluctuations (see Figure 26.7).
To calculate the profit factor, in cell J5 type:
(SUMIF(K11:K128,">0")SUMIF(U11:U128,">0")
316
SUMIF(AE11:AE128,">0"))/(SUMIF(K11:K128,"<0")SUMIF(U11:U12
8,"<0")
SUMIF(AE11:AE128,"<0"))
Before we can calculate the evaluation variables in Figure 26.5, we need
to know what a specific f will mean for each trade in the spreadsheet. Figure
26.6 shows what an f of 2 percent will do for the trades recorded in Figure 26.3.
In this case, a starting balance of $100,000 and an f of 2 percent means that we
should buy 1,000 shares for a total value of $32,000, and that the actual amount
we’re risking to lose is $750. As the trade develops over the next several days,
we go from an open profit of $1,980 to a closed-out profit of $7,980, with the
costs for the trade also taken into consideration, as specified in cell C4 in
Figure 26.4.
Note that the total risk for this trade is $750, which corresponds to only 0.75
percent of the total amount going into the trade. This is because the stop loss is
closer to the entry price than the money management point, which is a necessity
for a short-term system to be able to trade as many markets as possible.
To calculate the number of shares, in cell Q11 type:
IF(AND(L11<>L10,L11>0), MIN(INT($AG10*$C$3/M11),
$AH10/$AF11/L11),IF(L110,0,Q10)), where column L denotes the entry
price, column AG denotes the total equity for the portfolio, cell C3 denotes
the fictive percentage risk per trade, column M denotes the MMP, column
AH denotes the available equity, and column AF denotes the number of
entry signals that day. (See Figure 26.3 for columns L and M, Figure 26.4
for cell C3, and Figure 26.7 for columns AG, AH, and AF.)
To calculate the amount tied up in the trade, in cell R11 type:L11*Q11
To calculate the actual amount risked in the trade, in cell S11 type:
N11*Q11, where column N denotes the stop loss.
To calculate the open profit or loss of the trade, in cell T11 type:
IF(Q11>0,O11*Q11$C$4,0), where column O denotes the open profit
or loss for one share, and cell C4 denotes the costs (see Figure 26.3).
To calculate the closed-out profit or loss of the trade, in cell U11 type:
IF(AND(Q110,Q10>0),P11*Q10-$C$4,0), where column P denotes the
closed-out profit or loss for one share (see Figure 26.3).
Highlight the cells in row 11 and drag down to fill the cells below with the
formulas in row 11, for as many cells as necessary to accommodate all trades in
all markets. Do the same for all other markets. In this case, the spreadsheet is prepared for three markets, with the data for Market 1 in columns B to F, the calculations for Market 1 in columns G to K, the data for Market 3 in columns V to Z,
and the calculations for Market 3 in columns AA to AE.
CHAPTER 26
317
Three items of importance to note about the formulas for Figure 26.6 are that
even though a trade is signaled on a one-share basis in columns L to P, in Figure
26.3, a trade still might not take place if all the money already is tied up in other
trades. Second, if the f is so high that the amount of capital needed to buy the
shares specified by f isn’t available, we will buy as many shares as possible, given
the money at hand, not already tied up in other positions.
Third, because all signals and trades are recorded at the end of a trading day,
there is no way to tell the true intra-day order of the trades in case the system gave
several signals in several markets during the same day. Therefore, the best compromise for our analysis is to split the money between these signals.
For example, if, at the end of one day, we have $30,000 available on the
account (not already tied up in any trades), but also three new signals, each one
asking for $20,000 from the available money, we will give each new signal
$10,000. After this, the available money will be zero, unless we have no closedout trades, which will transfer to the account the exit price of that market, multiplied by the number of shares in the closed-out trade.
Last, we need to calculate the combined result from all trades, open and
closed, on a daily basis, to find out how that will affect our portfolio as a whole.
This is done in columns AF to AL in Figure 26.7. First, we need to calculate the
number of new signals we have each day, so that we know how to divide the money
among them, according to the rules just described (column AF). Once that is done,
the account equity for each day is calculated as the previous day’s equity, plus the
change from one day to the next in the open profit or loss for all open trades, plus
the closed-out profit or loss from all trades closed out that day (column AG).
The available equity, in column AH, is calculated as the total equity, in column AG, minus the open profit or loss (column T, for Market 2), minus the initial
amount tied up in all open trades (column R, for Market 2). The daily percentage
fluctuations in the total equity are calculated in column AL. To calculate the drawdowns (in column AJ) and flat times (in column AK), we first need to calculate the
latest equity top in column AI.
To calculate the number of new entry signals, in cell AF11 type:
IF(AND(B11<>B10,B11>0),1,0)IF(AND(L11<>L10,L11>0),1,0)IF(
AND(V11<>V10,V11>0),1,0), where columns B and V denote the entry
price for Markets 1 and 3, respectively. (Markets 1 and 3 not shown.)
To start the portfolio equity calculation, in cell AG10 type: C2.
To calculate the portfolio equity, in cell AG11 type:
AG10SUM(J11J10,T11T10,AD11AD10)SUM(K11,U11,AE11),
where columns J and AD denote the open profit or loss for markets 1 and
3, respectively, and columns K and AE denote the closed-out profit or loss
for markets 1 and 3, respectively.
318
To start the available equity calculation, in cell AH10 type: AG10.
To calculate the available equity, in cell AH11 type:
AG11SUM(J11,T11,AD11)SUM(H11,R11,AB11), where columns H
and AB denote the tied up capital in trades in markets 1 and 3, respectively.
To start the equity top calculation, in cell AI10 type: AG10.
To calculate the equity top, in cell AI11 type: MAX(AG$10:AG11).
To calculate the drawdown, in cell AJ10 type: (AI10–AG10)/AI10.
To calculate the flat time, in cell AK10 type: IF(AJ10<0,AK91,0).
To calculate the daily return, in cell AL11 type: (AG11AG10)/AG10.
Highlight the cells in row 11 and drag down to fill the cells below with the
formulas in row 11, for as many cells as necessary to accommodate all trades in
all markets. Note that new columns must be added in case you add more markets
to the calculations, and that the column references for the portfolio calculations
will change depending on the number of markets used.
To get a more visual feel for the system, we can make a chart of the equity
curve, as in Figure 26.8, and a chart of the drawdowns as in Figure 26.9. All the
FIGURE
26.8
Equity curve chart.
CHAPTER 26
FIGURE
319
26.9
Drawdown underwater chart.
dips below the zero line in the drawdown chart correspond to the downturns in the
equity chart. Note in Figure 26.9 how the largest drawdown is only a tad larger
than the second largest drawdown, and how the system manages to trade itself out
of it and set another new equity high before the end of the testing period.
A few of these numbers change when we change the fictive f from 2 to 4 percent. First, note in Figure 26.10 how the available equity in row 11 goes down to
$10,040, as compared to $48,020 in Figure 26.7. This is because the amount tied
up in the two positions that day increased with the amount risked. In fact, in the case
of market 2, the suggested amount tied up, based on the total equity, increased to
an amount surpassing the amount available in Figure 26.10. Therefore, the amount
tied up in Figure 26.11 reaches its maximum of $50,000, which is calculated as the
amount available from the end of the previous day (cell AH10, in Figure 26.10),
divided by the number of new signals that day (cell AF11, in Figure 26.10).
A few rows in Figure 26.10 also indicate that no equity is available at the end of
that day, going into the next day’s trading (rows 25, 35, and 36). Had there been any
trades signaled for rows 26, 36, and 37, we would not have been able to take those
trades, simply because all our money would have been tied up in other trades already.
320
FIGURE
26.10
Changing f from 2 to 4 percent.
In Figure 26.11, note how the values of both the two winning trades and the
losing trades are larger than for the same trades in Figure 26.6. This is not always a
given, just because we’re risking more in the trades in Figure 26.11. Many times,
risking more might mean a faster equity growth and higher equity in the end, but it
also might mean a more volatile development, which means situations where the
equity may have dipped to such low levels that the dollar values of the positions are
lower, despite a higher risk per trade. A limited amount of capital available for new
positions also might limit the amount invested (and consequently also won or lost),
on those days where the system signals several new positions simultaneously.
Figure 26.12 shows the end result from trading these three markets with a
fictive f of 4 percent. As you can see, the total return is higher, but there defi-
CHAPTER 26
FIGURE
321
26.11
Changing f from 2 to 4 percent.
nitely was a price to pay for the higher return as compared to the return from
risking only 2 percent per trade in Figure 26.5. The first thing we notice is that
the largest drawdown is almost twice as deep in Figure 26.12 as in Figure 26.5.
The longest flat time also is six days longer. These changes can also be seen in
Figures 26.13 and 26.14. In Figure 26.14, the largest drawdown goes on for
another several days as compared to the largest drawdown in Figure 26.9. This
shows up on Figure 26.13 in the form of a more flattened out equity curve than
that in Figure 26.8.
The larger swings in the equity curve also show up as a lower risk–reward
ratio in Figure 26.12. That the larger price swings are mostly connected to the losing trades is evident from the lower profit factor, which, despite the higher profit,
322
FIGURE
26.12
End result of f—4 percent on three markets.
indicates that we now are losing proportionally more money in the losing trades.
The cost for making a profit has increased with the increased risk per trade.
However, this is not to say that the 2 percent risk per trade is the preferred
alternative. That is completely up to you to decide, after having tested the system
for different risk levels and comparing all the results in a way that feels most comfortable to you.
FIGURE
26.13
Flattened equity curve.
CHAPTER 26
FIGURE
26.14
Increased drawdown time.
323
CHAPTER
27
Spreadsheet Development
N
ow that we have learned how to build a simple spreadsheet to calculate f, let’s
look at a more professional version and what we can analyze with it. This spreadsheet is the one that I use to calculate the result for the systems in Active Trader
magazine. All the initial performance summaries in Part 2 were, for example, put
together with this spreadsheet. I wish I could show you how to put together a
spreadsheet like this, but there is simply too much going on here to make that possible. This spreadsheet can calculate the combined results from 2,500 days of trading (approximately 10 years) on 60 markets simultaneously.
Figure 27.1 shows the initial parameter setting that you can experiment with.
The initial equity, risk-per-trade multiple, and average commissions are the same
as those in Figure 26.3. To this, I have added the possibility to adjust for dividends
and for an interest rate earned on the money left on the account.
The max margin-to-equity ratio keeps the system from entering into any new
positions if this number is surpassed, to avoid having all money tied up in open
positions, if the unthinkable happens and everything starts to move against you.
The max drawdown and max monthly drawdown values let you stop trading midmonth if the drawdown reaches intolerable levels. In both cases, the trading
resumes at the beginning of the next month, but will only be allowed to continue
as long as the trading goes your way. The mean accepted return is used to calculate the Sortino ratio in Figure 27.2.
For the strategy summary and rolling time window return analysis I strived
to gather as much information as possible, similar to the Institutional Advisory
Services Group (IASG) Web site. Figures 27.4 to 27.7 show the Web site.
325
326
FIGURE
2 7.1
Initial parameter settings.
In Figure 27.2, the ending equity and the total return are the same as those in
Figure 26.3. The average annual return is the compounded (or geometric) return,
which means the calculation makes use of the profits from previous years going
into each new year. The gain-to-loss ratio is similar to the profit factor, but instead
of dividing the gross profit by the gross loss, the gain-to-loss ratio divides the
average gain over a specific length (a month) of winning periods, with the average
loss over the same-length losing periods.
The winning months show the percentage of all months that end up with
a profit. Remember, often it is more important to have a high percentage of
winning months, rather than a high percentage of winning markets or trades.
The maximum drawdown and flat times are the same as in Figure 26.5,
except the flat time is expressed in months instead of days. The average drawdown
sums all the deepest points (one per drawdown) in all drawdowns and divides by
the number of drawdowns.
The Sharpe ratio is the average growth rate in the equity per month, minus
the risk-free interest rate (as defined in Figure 27.1), divided by the standard deviation of the monthly returns. The Sortino ratio is another risk–return ratio that
compares the monthly returns above a certain threshold level (see Figure 27.1)
with those below the same level.
CHAPTER 27
FIGURE
327
2 7. 2
The strategy summary for the professional spreadsheet.
The maximum and average margin requirements show how much of the total
equity is tied up in one or several positions, as the highest value over the whole
testing period or as an average for all days tested, including those days when we
have no open positions at all. The time in market shows how much time the entire
strategy, made up of all systems and markets tested and the average of all systemmarket combinations, spent in a trade.
Of the numbers mentioned, those to take most notice of are the average annual return in relation to the Sharpe ratio, the maximum drawdown and flat time in
relation to the average drawdown, the gain-to-loss ratio, and the percentage of winning months. The rest of the numbers grouped under Trade statistics, Trade frequency, Distribution analysis, and Miscellaneous are less important, simply because it’s
too much to keep track of, rank against everything else, and compromise between.
For example, if a strategy has a skewness and kurtosis I am not all that happy
with, but otherwise shows a good profit potential and a low risk, I am not about to
328
FIGURE
2 7. 3
Rolling time window analysis for the professional spreadsheet.
start tweaking that system any further to come to grips with the skew and kurtosis. I’d rather start working on a new system to see if I can combine new systems
and markets to come up with a new strategy that also has good skew and kurtosis
figures. If that doesn’t work either, so be it. I think you already have discovered
that to build and research a system, combine several systems and markets into a
whole strategy, and incorporate fixed fractional money management rules can be
as complex and time consuming as you want it to be.
Just to show you the complexity of the formulas going into this spreadsheet,
this formula calculates the amount risked in a trade for one market at a specific
point in time:
IF(AND(INDEX(NewSignals,ThisRow)>0,INDEX(EntryM4,ThisRow)<>
INDEX(EntryM4,ThisRow1),INDEX(EntryM4,ThisRow)>0),
MIN(INT(INDEX(TradeableEquity,ThisRow–1)*WeightM4*PercentRisk2/
(INDEX(RiskM4,ThisRow)*PointValM4))*IF(MarginReqM40,
INDEX(EntryM4,ThisRow),MarginReqM4),IF(MarginReqM40,INDEX(Trade
ableEquity,ThisRow1)*(1/INDEX(NewSignals,ThisRow)),
CHAPTER 27
329
INT(INDEX(TradeableEquity,ThisRow1)*(1/INDEX(NewSignals,ThisRow))/
MarginReqM4)*MarginReqM4)),IF(INDEX(ProfitM4,ThisRow)0,
INDEX(CommM4,ThisRow–1),0))
This formula calculates the accrued interest:
INDEX(AvailableEquity,ThisRow)*((1InterestRate2)^(1/365)1)
This formula calculates the bottom of a drawdown:
IF(INDEX(FlatTime,ThisRow)>INDEX(FlatTime,ThisRow1),
MIN(INDEX(Drawdown,ThisRowINDEX(FlatTime,ThisRow)1):
INDEX(Drawdown,ThisRow)),"")
Note that none of the formulas makes use of any normal cell references, such
as “B14,” referring to the cell in column B, row 14. To speed up the computing
time and to simplify error checking, I have given all the input and output variables
specific names, just as one would do to program the entire analysis spreadsheet in
a regular programming language, such as Visual Basic or Delphi.
Figures 27.4 to 27.7 are taken from the IASG Web site (www.iasg.com) and
are provided just to give you something to compare with. IASG is a Chicago-based
brokerage company that also tracks and publishes the results of many commodity
trading advisors and fund managers. The IASG Web site also has a comprehensive
help page that describes and shows the calculations behind many of the evaluation
variables used.
Other companies that also track many CTAs and fund managers include
The Barclays Group (www.barclaygrp.com), Van Hedge Fund Advisors
(www.hedgefund.com), Hedgefund.net (www.hedgefund.net), Hedgefund247
(www.hedgefund247.com), International Traders Research (www.managedfutures
.com), and Risk & Portfolio Management (www.rpm.se) in Sweden.
The numbers in Figures 27.4 to 27.7 are all real performance numbers from
real fund managers and CTAs. Note that several performance numbers in these
figures can’t be found in my spreadsheet in Figures 27.2 and 27.3, such as the
monthly performance summary in Figure 27.2 and several of the different ratios
in Figure 27.3. The time-window analysis in Figure 27.6 is basically the same as
that in Figure 27.3, except Figure 27.3 also holds the annualized numbers. Some
of the information in Figures 27.4 to 27.7 also is redundant, such as the monthly
numbers in Figure 27.4 and the chart of the monthly ROR at the bottom left in
Figure 27.7.
Figure 27.7 shows a few charts that also can be found on the IASG Web site.
The top left chart shows the equity growth of a specific advisor, while the bottom
right chart shows the drawdowns. These are essentially the same charts as those we
put together in Figures 26.8 and 26.9, and 26.13 and 26.14. They are also essen-
330
FIGURE
2 7. 4
The IASG Web site.
tially the same as those in Figures 27.8 and 27.9, which are made with the help of
my own professional spreadsheet.
The monthly distributions in the top right chart in Figure 27.7 illustrate
the same thing as Figure 27.10 from my professional spreadsheet. Note especially in Figure 27.7 how close to a normal distribution the monthly returns
are, and remember what we learned in Part 3—the returns over specific periods of time should be normally distributed around an average profit per
CHAPTER 27
FIGURE
331
2 7. 5
The IASG Web site.
month, not the trades themselves, which should have a set of few very specific outcomes.
Finally, we’ve already looked at the monthly return chart at the bottom left
corner in Figure 27.7. The professional spreadsheet’s version of the same chart can
be seen in Figure 27.12, which also holds the same information as the monthly
performance numbers in Figure 27.4 and similar type of information as the timewindow numbers in Figures 27.3 and 27.6. Aside from all the charts mentioned,
332
FIGURE
2 7. 6
The IASG Web site.
my professional spreadsheet also has a chart over the drawdown distribution, as
shown in Figure 27.11, which holds parts of the information that the IASG drawdown analysis holds (not shown).
Aside from the portfolio analysis, the spreadsheet also can look at the individual markets to help you get a feel for how they interact with each other and the
portfolio as a whole. The most interesting numbers here are the percentage contribution and the percentage correlation, in Figure 27.14. The percentage contribution number shows how large the profit or loss is in an individual market in
relation to the total profit or loss of the portfolio. The percentage correlation
number shows how much the equity curve of the individual market correlates
with the total equity.
However, because all markets are dependent on each other, the relationships
between the results for the individual markets and the portfolio as a whole are not
CHAPTER 27
FIGURE
333
2 7. 7
The IASG Web site.
linear, so that, for example, a positive equity for one market will not always mean
a positive contribution to the portfolio equity. Instead, it all depends on where and
when all the contributions, in the form of winning and losing trades, happen in
relation to each other.
For example, a market with a negative contribution and a negative correlation still might add positively to the overall result, because of its tendency to be
profitable when all other markets are not. This helps keep up the portfolio equity
and allows for larger positions in the other markets, once they start to function
again.
FIGURE
2 7. 8
Total equity curve from spreadsheet.
FIGURE
2 7. 9
Drawdown curve from spreadsheet.
334
FIGURE
2 7.10
Monthly distributions from spreadsheet.
FIGURE
2 7.11
Distribution of drawdowns from spreadsheet.
335
336
FIGURE
2 7.12
Cumulative monthly returns from spreadsheet.
Likewise, just because a market has a high positive contribution doesn’t
mean that it was the market that functioned best throughout the entire testing period. It might have been that it didn’t work at all for the first half, when the portfolio equity was relatively low but increasing because of profits from other markets.
However, it might have functioned very well during the second half, when the
portfolio equity was relatively high, which would have allowed for larger positions
and thereby larger profits during this period.
The spreadsheet allows you to test this by setting the market weight to zero,
as in Figure 27.13. Doing so for, for example, all losing markets in a portfolio will
most likely produce new losing markets out of the original winning markets.
Excluding these markets will most likely produce a new set of losing markets, and
so on, no matter if these markets had positive average profit per trade when analyzed in TradeStation.
Sometimes, taking away the losing markets will even lower the final profit
for the portfolio, and sometimes it’s even a good idea to throw in a couple of losing markets to the mix, to either increase the final profit for the portfolio or even
out the equity growth, which would result in a higher Sharpe ratio and the possibility for more aggressive trading.
In short, because all markets are dependent on one another, there are no sure
winners or losers. It all depends on where and when all individual markets’ prof-
CHAPTER 27
FIGURE
337
2 7.13
First part of individual market summary.
FIGURE
2 7.14
Second part of individual market summary.
its and losses came in relation to the equity of the portfolio. Altering the fractional amount risked per trade also might change things around.
MONEY MANAGEMENT EXPORT CODE
Figure 27.15 shows what the raw data look like for one market on a one-share
basis. Figure 27.15 is similar to Figure 26.3, except that the stop loss and money
management point (MMP) distances are excluded and replaced by the risk column
(column L). In this case, the risk column holds the distance between the entry price
(column K) and the MMP. Columns M and N hold the open and closed-out profits at the end of the day. In this case, the stop-loss distance isn’t necessary for the
calculations, but when it is, it will be the same as the MMP distance and show up
in the risk column. The data in Figure 27.15 can either be entered manually one
day at a time for one market at a time (there is room for 60 system–market combinations), or imported from TradeStation with the help of a special export function created in TradeStation’s EasyLanguage, which can look as follows:
338
FIGURE
2 7.15
Raw data for one market, one-share basis.
{The RiskCalc variable is necessary for the Money Export function, and should be
placed adjacent to the stops and exits.}
{1} Variable:
RiskCalc(0);
RiskCalc = TrueRange * 4;
{Money management export, with Normalize(False). SetMoneExport(True).}
CHAPTER 27
339
Variables:
{2} MoneyExport(True);
If MoneyExport = True Then Begin
Variables: MP(0), TT(0), FileName(""), TradeString(""), OldString(""),
FirstExpDate(0), Missing(0), FillDate(0), SteppinIn(0), PosProfit(0),
ClosedProfit(0), StopLoss(0), RiskValue(0), ExcelMonth(0), ExcelDay(0),
ExcelYear(0), ExcelDate("");
FileName = "D:\Temp\Optisize-" +
RightStr(NumToStr(CurrentDate, 0), 4) + "-" +
LeftStr(GetSymbolName, 4) + ".csv";
FileDelete(FileName);
TradeString = "Date" + "," + LeftStr(GetSymbolName, 8) + "," +
"Risk ($)" + "," + "Open ($)" + "," + "Close ($)" + NewLine;
FileAppend(FileName, TradeString);
FirstExpDate = DateToJulian(LastCalcDate) - 2500 * 1.4;
If DateToJulian(Date) >= FirstExpDate Then Begin
For Missing = FirstExpDate To (DateToJulian(Date) - 1) Begin
FillDate = JulianToDate(Missing);
If DayOfWeek(FillDate) > 0 and
DayOfWeek(FillDate) < 6 Then Begin
ExcelMonth = Month(FillDate);
ExcelDay = DayOfMonth(FillDate);
ExcelYear = Year(FillDate);
If ExcelYear >= 100 Then
ExcelYear = 2000 + (ExcelYear - 100);
ExcelDate = NumToStr(ExcelMonth, 0) + "/" +
NumToStr(ExcelDay, 0) + "/" + NumToStr(ExcelYear, 0);
TradeString = ExcelDate + "," + "0" + "," +
"0" + "," + "0" + "," + "0" + NewLine;
If TradeString <> OldString Then
{4}
OldString = TradeString;
End;
End;
End;
End;
340
{5} If DateToJulian(Date) >= FirstExpDate Then Begin
If DateToJulian(Date) - DateToJulian(Date[1]) > 1 Then Begin;
For Missing = (DateToJulian(Date[1]) + 1) To (DateToJulian(Date) - 1)
Begin
FillDate = JulianToDate(Missing);
If DayOfWeek(FillDate) > 0 and
DayOfWeek(FillDate) < 6 Then Begin
ExcelMonth = Month(FillDate);
ExcelDay = DayOfMonth(FillDate);
ExcelYear = Year(FillDate);
ExcelDate = NumToStr(ExcelMonth, 0) + "/" +
NumToStr(ExcelDay, 0) + "/" + NumToStr(ExcelYear, 0);
TradeString = ExcelDate + "," + NumToStr(SteppinIn[1], 4) +
"," +
NumToStr(RiskValue[1], 4) + "," + NumToStr(PosProfit[1],
4) + "," +
"0" + NewLine;
End;
End;
End;
{6} ClosedProfit = 0;
SteppinIn = 0;
RiskValue = 0;
PosProfit = 0;
End;
If MarketPosition <> 0 Then Begin
SteppinIn = EntryPrice;
RiskValue = RiskValue[1];
If MarketPosition = 1 Then
PosProfit = Close - EntryPrice;
If MarketPosition = -1 Then
CHAPTER 27
341
PosProfit = EntryPrice - Close;
End;
MP = MarketPosition;
TT = TotalTrades;
If TT > TT[1] and MP <> MP[1] Then Begin
If MP[1] = 1 Then
ClosedProfit = ExitPrice(1) - EntryPrice(1);
If MP[1] = -1 Then
ClosedProfit = EntryPrice(1) - ExitPrice(1);
End;
If SteppinIn <> SteppinIn[1] and SteppinIn > 0 Then
RiskValue = RiskCalc;
{7} ExcelMonth = Month(Date);
ExcelDay = DayOfMonth(Date);
ExcelYear = Year(Date);
ExcelDate = NumToStr(ExcelMonth, 0) + "/" + NumToStr(ExcelDay, 0) +
"/" + NumToStr(ExcelYear, 0);
TradeString = ExcelDate + "," + NumToStr(SteppinIn, 4) + "," +
NumToStr(RiskValue, 4) + "," + NumToStr(PosProfit, 4) + "," +
NumToStr(ClosedProfit, 4) + NewLine;
End;
End;
Because we already have stepped through a few pieces of code, I will keep the
comments brief.
1.
2.
The RiskCalc variable must be added to the system code (preferably adjacent
to the stops and exits) to calculate the MMP.
The variable MoneyExport(True) must be placed on top of the code or even
as an input. The other variables will only become active when MoneyExport
is set to True. To speed up the computing time, the program will not run
through the rest of the code as long as MoneyExport is set to False.
342
3.
4.
5.
6.
7.
The first part of the code only needs to be done once, on the very first bar on
the chart. Within that part of the code, we make sure that the first day to be
exported is 2,500 days prior to the last day of the chart.
This code also transforms the TradeStation data format to Excel date format.
The first piece of code that needs to be repeated for every bar makes sure that
all data from all markets are synchronized and will fill in all missing days,
such as holidays, with yesterday’s data. It too transforms the TradeStation
data format to Excel date format.
The code now starts to look for position changes and alters the values of the
variables to be exported, depending on how the position changes from day
to day.
The final daily export starts with another transformation of TradeStation
dates to Excel dates.
CHAPTER
28
Combined Money Market Strategies
W
ith all the bits and pieces in place, let’s bring things to a conclusion by looking
at a few combinations of our short-term systems and long-term filters, when tested using dynamic ratio money management. In doing so, we will try to optisize
most of them in relation to the Sharpe ratio. That is, we will try to come up with
the fictive f to risk per trade in relation to the distance between the money management point and the entry price for each market in each trade, which gives us
the highest possible return in relation to the standard deviations of the returns.
Remember that the money management point will be placed four true ranges
away from the entry price only so that we can calculate the number of shares to
buy and the amount of the available capital to tie up in the trade. The actual risk
(f) per trade will be less and vary with the behavior of the market, in accordance
with the stop and exit rules for each version of the systems.
To do this, I have used the same type of tables and charts that are featured in
the systems lab pages in every issue of Active Trader magazine. Unfortunately, the
Sharpe ratios are not shown in any of them, but will be mentioned in the text after
they have been derived from each strategy’s summary table, similar to that depicted in Figure 27.2. In those cases where I haven’t optisized in accordance with the
Sharpe ratio, it still will be mentioned for comparison purposes.
Also, remember that we don’t have to optisize in relation to the Sharpe ratio,
but could just as well have decided to focus on any of the other performance parameters in Figure 27.2, such as the total return, the profit factor, the drawdown or the
flat time, or any combination or compromise between two or several of these and
other variables.
When looking at these strategies, this is also the first time we will take a closer look at the drawdown and use it as an input in our evaluation process. We have
343
344
not done so before because the drawdown is not a core system characteristic. It
still isn’t, and we are not optisizing any of the strategies in accordance with it, but
because the latest bear market has made all the strategies lose money over the last
several months, we will discuss briefly how any eventual changes to either the systems or the strategies could lower the short-term drawdowns without also decreasing the speed of the long-term equity growth.
One important distinction I try to make when tying everything together is to
look at the complete picture as a strategy as opposed to a system. Therefore, when
I talk about the strategy, I mean the entire trading machine, including the system
with its entry and exit rules, the (trend) filter, the markets traded, and the money
management. When I talk about the systems, I mean only the entry and exit rules,
and sometimes only the entry rules.
The stocks used for this testing are the same as those used throughout the
rest of the book—the 30 Dow stocks and 30 of the most liquid NASDAQ
stocks. However, because Intel and Microsoft belong to both these groups, I
group these two stocks with the NASDAQ stocks only, so that the group of Dow
stocks consists of only 28 stocks. I also won’t test any of the strategies on any
of the indexes.
In total, I will test 12 different strategies that can be subdivided into four different groups based on the long-term filters. The first six strategies will use the RS
system No. 1, with the number of system–market combinations (symacs) varying
between 56 and 60 (except for Strategy 4, which has 30), depending on whether
the testing uses all stocks from both groups or uses two different systems on the
same group of stocks.
Group number two is made up of two strategies tested on 60 symacs each,
using the relative-strength bands as the filter. The next two strategies use the rotation as the filter and have also been tested on 60 symacs each. So have the last two
strategies that use both the relative-strength bands and the rotation as filters, working independently of each other.
To avoid becoming too redundant, I have tried to spread out the learning
experience over all the strategies, so that I won’t talk about every single aspect of
the evaluation of the results for each and every strategy. For example, we really
won’t take a closer look at the time-window return analysis until the very last strategy. Hopefully, this also will entice you to jump back and forth between the different strategies to get better practice in how to compare them with each other. For
a few of the strategies, I also decided to leave out some of the charts and tables.
When looking at several different strategies or fund managers, it is a good
idea to compare them not only with one another but also with a few benchmark
indexes. Table 28.1 gives you the most important and basic information for the
three most commonly used stock market indexes, over the same time period as we
tested our strategies. Our goal for all our strategies is to at least do better than the
closest comparable index on every one of these evaluation parameters.
CHAPTER 28
TAB LE
345
28.1
Benchmark Comparisons, January 1993–July 2002
Index
Dow Jones
S&P 500
NASDAQ 100
Annual comp. return
Sharpe yearly
9.68%
0.65
7.09%
0.40
9.50%
0.22
Max drawdown
Longest flat time
36%
30 months
50%
27 months
82%
27 months
Profitable months
63%
61%
56%
Before we comment on the results of the strategies, a few things must be
noted. First, note in Table 28.2 that the number of trades with the money management added is slightly less than the amount that could have been expected from
Table 21.3, which comes out to 8,352 (144 * 58), because a few trades signaled
before we attached the money management and could not be taken because of the
financial constraints we applied to the strategy. The signals are still there, but
because we were already fully invested, we couldn’t take the trades.
Second, the trades missing, combined with a few missing markets (the indexes), also lower the number of profitable trades. Another reason for a lower percentage of profitable trades is that we have added a cost of $20 per trade, which
we need to make up for before any individual trade can show a profit.
Third, the profit factor is now at 1.23, which is lower than the 1.32 in Table
21.3. This, too, is a consequence of a lower percentage of profitable trades and the
added costs. But even more so, it is a direct consequence of the money management. By altering the amount risked per trade, we also alter the relative size of the
winners and losers, which in turn alters the profit factor.
The average trade length and total time spent in a trade also are much shorter in Table 28.2 than in Table 21.3. As mentioned in Part 3, this is because, in Table
21.3 we also count holidays and weekends, which are excluded in Table 28.2.
STRATEGY 1
■
■
■
Long-term filter: RS system No. 1
Short-term systems: The stop-loss version of the Meander system v. 1.0
Markets: 28 Dow stocks, 30 NASDAQ stocks, for a total of 58 systemmarket combinations (symacs)
Tables 28.2 and 28.3, and Figures 28.1 and 28.2 show the results for this
strategy traded on the 58 stocks used for the research. (For the initial research, we
used 30 stocks each from the Dow Jones Index and NASDAQ 100 index, with
Intel and Microsoft in both groups.) To give you a feel for how this strategy has
346
TAB LE
28.2
Strategy Summary
Profitability
Trade statistics
End. equity ($):
Total return (%):
8,446,897
745
Avg. annual ret. (%):
Profit factor:
Avg. tied cap (%):
Win. months (%):
Drawdown
Max DD (%):
Longest flat (M):
No. trades:
Avg. trade ($):
24.94
1.23
Avg. DIT:
Avg. win/loss ($):
73
66
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
21.8
15.5
7,029
1,059
11,003
148,187
100
5.8
(9,945)
(118,190)
50.8
27.9
12.2
61.1
evolved over the course of the book, you can compare these results with those in
Tables 10.5, 20.3, and 21.3.
As with most strategies featured here, this one is optisized to maximize the
Sharpe ratio, which in this case comes out to 1.31, with the fictive f set to 3 percent per trade.
With an average annual return of close to 25 percent and a maximum drawdown of 22 percent, this strategy seems to function really well. The percentage of
winning months is at a decent 66 percent, which is considerably higher than the
percentage of winning trades. This means that the system is doing a good job of
TAB LE
28.3
Rolling Time-window Return Analysis
Cumulative
12 months
24 months
36 months
48 months
60 months
Most recent:
–5.22%
–15.84%
34.89%
102.16%
139.34%
Average:
Best:
28.51%
60.28%
70.85%
140.21%
128.87%
218.43%
203.80%
316.52%
300.38%
425.26%
Worst:
St. dev:
–14.19%
18.98%
–15.84%
31.32%
34.89%
37.85%
89.03%
48.38%
138.81%
72.51%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–5.22%
28.51%
–8.26%
30.71%
10.49%
31.78%
19.24%
32.02%
19.07%
31.98%
Best:
Worst:
60.28%
–14.19%
54.99%
–8.26%
47.12%
10.49%
42.86%
17.26%
39.34%
19.02%
St. dev:
18.98%
14.59%
11.29%
10.37%
11.52%
CHAPTER 28
FIGURE
28.1
Strategy 1 equity curve.
FIGURE
28.2
Strategy 1 drawdown curve.
347
348
cutting the losses short and letting the profits run, to create profitable trading periods rather than profitable trades.
The rolling time-window analysis shows no losing three-year trading
sequence and that the latest sequence, with an annualized return of 10.5 percent,
actually is the worst one over the entire testing period—which occurred during the
current bear market. Note that in Figures 28.1 and 28.2, the current drawdown is
not the worst one and, despite the fact that this is a long-only strategy, it has coped
really well with the current bear market.
The worst drawdown happened sometime in late summer 2001, but since
then we also have had a new equity high, which indicates that the strategy is capable of making money even during the most adverse times. Granted, Figure 28.1
shows that the equity growth has come to a halt since mid 2000, and more or less
just fluctuated between 8 and 10 million, which probably would have scared off
many investors, but compared to a buy-and-hold strategy, there is no doubt that
this strategy can hold its own.
The robustness of the strategy also shows in the period preceding the latest
bear market during which the maximum drawdown surpassed the 10-percent level
only twice. I would most definitely trust this strategy in the future, but probably
modify it so that it would trade the short side as well, or combine it with a strategy that does. This would most likely decrease the average annual return in a bull
market, but because it also would increase it in a bear market, it is likely that the
overall return over a longer period of time remain approximately the same.
Also remember that both the return and the drawdown are functions of how
much we risk per trade. By decreasing the risk, both the return and the drawdown
numbers will be lower. Therefore, it also is fully possible to first analyze and then
trade the strategy so that you lower the risk per trade when it is evident the behavior of the market has changed into unfamiliar ground for the strategy.
Note that the time in the market per symac is approximately 25 percent,
which means that, theoretically, we need four markets to be in a trade all the time.
With the fictive f at 3 percent and the MMP on average 15 percent away from the
entry price, Figure 26.1 tells us we can be in only five trades simultaneously on
average. If we multiply the theoretical number of markets to track to allow us to
be in trade at all times by the number of markets we can be in simultaneously, we
get 20.
Because this strategy monitors 58 markets, the strategy probably has to skip
a lot of trades or risk a smaller than optimal amount because of the lack of available capital. To come to grips with this, we probably need to place the MMP further way from the entry price and revise the research, risking a little less per trade.
For example, Figure 26.1 tells us that by placing the MMP 20 percent away from
the entry price and risking 2.25 percent per trade, we should be in eight trades
simultaneously. The added trades should help us increase the return and the Sharpe
ratio even further. I leave this to you to research on your own.
CHAPTER 28
349
STRATEGY 2
■
■
■
Short-term systems: Both stop-loss and trailing-stop versions of the
Meander system v. 1.0
Markets: 28 Dow stocks, for a total of 56 symacs
Tables 28.4 and 28.5, and Figures 28.3 and 28.4 show the result from trading both
the stop-loss version and the trailing-stop version of the Meander system on the
Dow Jones stocks. In this case, we take the initial $1,000,000 to $2.9 million, for
an average annual return of 11.72 percent over the 10-year testing period. The
Sharpe ratio came out to 1.42.
TAB LE
28.4
Strategy 2 Results
Profitability
Trade statistics
End. equity ($):
Total return (%):
2,892,596
189
Profit factor:
Avg. tied cap (%):
Win. months (%):
Drawdown
Max DD (%):
Longest flat (M):
TAB LE
11.72
1.26
53
69
No. trades:
Avg. trade ($):
10.8
9.9
Avg. DIT:
Avg. win/loss ($):
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
24 months
36 months
7,176
264
2,310
29,226
100
6.0
(1,950)
(17,471)
48.2
30.6
12.5
62.4
28.5
Strategy 2 Time-window Analysis
Cumulative
12 months
48 months
60 months
Most recent:
–4.28%
–0.54%
16.20%
29.06%
48.57%
Average:
Best:
13.24%
34.89%
30.73%
54.36%
51.44%
82.71%
74.58%
110.11%
101.28%
132.33%
Worst:
St. dev:
–4.69%
8.26%
–0.54%
12.03%
16.20%
16.60%
24.47%
21.44%
46.36%
22.14%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–4.28%
13.24%
–0.27%
14.34%
5.13%
14.84%
6.59%
14.95%
8.24%
15.02%
Best:
Worst:
34.89%
–4.69%
24.24%
–0.27%
22.25%
5.13%
20.40%
5.63%
18.36%
7.92%
St. dev:
8.26%
5.85%
5.25%
4.98%
4.08%
350
FIGURE
28.3
FIGURE
28.4
CHAPTER 28
351
The strategy was tested with a 1.5 percent risk per trade: when any of the
exits for the trailing-stop version of the system were hit, two-thirds of the position
were exited, corresponding to 1 percent of the original risk. When any of the stoploss exits were hit, the position was decreased by what corresponded to 0.5 percent risked of the original position. Using both versions of the system with asymmetric exit rules helps us make the most out of each trade. In this case, we can take
a profit as soon as one of the stops or one of the profit targets is hit. Thus, we can
remain in the trade with a small position and wait for the market to make the most
out of the entry signal we trust.
Compared to the version in Tables 28.2 and 28.3, this version of the system
does an even better job of cutting losses and letting profits run, which shows in a
lower number of profitable trades (48 percent), but at the same time an even higher number of profitable months (69 percent).
The maximum drawdown is also very low, at a modest 10.8 percent, which
is also the drawdown we currently happen to be in. Aside from this drawdown, the
maximum drawdown has rarely surpassed 8 percent. However, despite the fact that
we happen to be in the maximum drawdown, judging from the slope of the equity
curve in Figure 28.3, it doesn’t look like the equity growth has stalled the same as
it has in Figure 28.1, although it is obvious the strategy did slightly better prior to
the current bear market.
The fact that the system currently is in its worst drawdown also indicates
that it is the markets not traded that did the best lately. That is, despite the recent
free-fall in the NASDAQ stocks, it is largely due to the NASDAQ stocks that the
strategy managed to produce the recent equity high in Figure 28.1 and avoid
falling into a new maximum drawdown afterwards. This further confirms the
strategy’s ability to find good, or at least decent, trading opportunities in the
most adverse environments, thus helping us to stay afloat while waiting for better times.
Note that the time in the market per symac is approximately 30 percent,
which means that theoretically we need three symacs to be in a trade all the time.
With the fictive f at 1.5 percent and the MMP on average 15 percent away from
the entry price, we can be in 10 trades simultaneously on average. If we multiply
the theoretical number of symacs to track to be in a trade at all times by the number of symacs we can be in simultaneously, the answer is 30. (I decided to place
the MMP 15 percent away from the entry price based on the assumption that each
symac should spend about 20 percent in the market.)
In this case, we are tracking 56 symacs. Normally, this means that we should
increase the distance between the MMP and the entry price to allow for more open
trades at any one time, but because this strategy consists of two systems with identical entry rules, we are doing fine. The strategy is doing a good job of balancing
the trade size with the number of markets tracked and the possibility to trade at
any one time.
352
STRATEGY 3
■
■
■
Short-term systems: The trailing-stop version of the volume-weighted average system
Markets: 28 Dow stocks, 30 NASDAQ stocks for a total of 58 symacs
This strategy has been tested on all 58 stocks, with a fictive risk of 2 percent for
the Dow stocks and 6 percent for the NASDAQ stocks. The asymmetrical risk
between the two groups of stocks is another way of making the most out of the system and the markets it is applied to. The Sharpe ratio for this strategy comes out
TAB LE
28.6
Strategy 3 Results
Profitability
Trade statistics
End. equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. months (%):
Drawdown
Max DD (%):
Longest flat (M):
TAB LE
2,767,231
177
11.21
1.14
55
61
28.9
23.0
No. trades:
Avg. trade ($):
Avg. DIT:
Avg. win/loss ($):
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
9,504
144,675
99
2,904
609
4.6
(9,715)
(124,133)
51.5
9.2
5.1
25.3
28.7
Cumulative
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
Best:
–14.33%
14.58%
42.05%
–27.86%
34.74%
85.23%
1.71%
59.26%
112.12%
33.63%
87.46%
156.93%
46.37%
120.36%
171.25%
Worst:
St. dev:
–18.50%
13.78%
–27.86%
19.82%
1.71%
21.09%
28.95%
27.03%
46.37%
27.51%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–14.33%
14.58%
–15.06%
16.08%
0.57%
16.78%
7.52%
17.01%
7.92%
17.12%
Best:
Worst:
42.05%
–18.50%
36.10%
–15.06%
28.49%
0.57%
26.61%
6.56%
22.09%
7.92%
St. dev:
13.78%
9.46%
6.59%
6.16%
4.98%
CHAPTER 28
FIGURE
28.5
The equity curve for Strategy 3.
FIGURE
28.6
The drawdown curve for Strategy 3.
353
354
to 0.81. Tables 28.6 and 28.7 can be compared to Tables 13.5, 19.1, and 20.5,
which show the result during the development of the system.
Comparing the numbers in Tables 28.6 and 28.7 and Figures 28.5 and 28.6
with the numbers for the strategies we’ve already looked at, it’s apparent that this
strategy is not as good as the previous two. For one thing, both the average annual return and the profit factor are the lowest, while the maximum drawdown is the
highest so far. To achieve these numbers, we also have to risk more, especially in
the NASDAQ stocks. Together with the lower Sharpe ratio, this indicates that
we’re not getting as much bang for the buck as with the other strategies.
However, the fact that we can risk more on the NASDAQ stocks to maximize
the Sharpe ratio also indicates that the system is relatively safe to trade on these
markets. Remember that the optimal f, when optimizing the equity growth, is an
indication of how large we can allow our largest loser to be while still ending up
at the highest possible equity level.
Nonetheless, the strategy has not coped well with the latest bear market and
is currently in its worst drawdown, at close to 30 percent. This fact, combined with
a longest flat time of 23 months, is bad enough to discourage many professional
traders and money managers to trade this strategy as is. Thus, it doesn’t matter that
the strategy has done much better than a buy-and-hold strategy on any of the market indexes. (Don’t forget to compare the strategy results for all strategies with the
numbers in Table 28.1.)
To trade this strategy, we need to either come up with a way to trade it on the
short side as well, or combine it with another short-selling strategy. This new strategy should then be able to deliver a higher risk-adjusted return (the Sharpe ratio)
to a lower risk per trade, to make trading it worthwhile when compared to the
Meander strategies.
STRATEGY 4
■
■
■
Short-term systems: The trailing-stop version of the volume-weighted average system
Markets: 30 NASDAQ stocks for a total of 30 symacs
Just to show you what you can do with the spreadsheet used for these calculations
and how the results can vary with the risk per trade, I traded the trailing-stop version of the volume-weighted average system on the NASDAQ stocks only, setting
the fictive risk to 50 percent.
Table 28.8 shows that the average annual return equals 32.5 percent, but also
that the largest drawdown, which actually happened in early 2000, surpasses 40
percent (see also Figure 28.7). Interestingly, despite the high risk per trade, the
Sharpe ratio still comes out to 0.76, which isn’t too bad. Another indication that
CHAPTER 28
TAB LE
355
28.8
Strategy 4 Results
Profitability
End. equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. months (%):
Drawdown
Max DD (%):
Longest flat (M):
Trade statistics
14,900,205
1,390
No. trades:
Avg. trade ($):
32.56
1.21
Avg. DIT:
Avg. win/loss ($):
61
55
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
42.3
13.3
692
20,087
230,028
4.7
(227,551)
2,194,892 (2,437,892)
53.8
73
4.4
2.4
6.0
the strategy is holding up really well in the current market is the fact that it has
managed to set two new equity highs since the worst drawdown, with another
drawdown of close to 40 percent in between. The drawdown chart (not shown) also
shows that the current drawdown is only the fourth worst drawdown since the start
of the testing period, surpassed also by the drawdown in 1999, prior to the sharp
run up in equity due to the bull market in late 1999 and early 2000.
FIGURE
28.7
356
Naturally, had I risked less, the drawdowns would have been smaller, but so
would the ending equity and possibly the Sharpe ratio also. Only the most riskseeking trader would trade this strategy as it stands here and now; for the rest of
us, it only serves as a good illustration of how risk and return go hand in hand.
Note also in Table 28.8 that the total number of trades comes out to 692,
which translates to only 23 trades per market tested over the entire testing period.
However, looking at Table 21.4, we can see that the system itself produces as many
as 62 signals per market over the same period. This means that only every third
signal will actually end up as a trade because of equity constraints.
Decreasing the fictive f will allow for more trades and a higher Sharpe ratio
and possibly also a higher return. Thus, even though we’re making some 32 percent per year, in this case we might be able to make more while risking less. This
is yet another little thread I leave for you to look into.
STRATEGY 5
■
■
■
Short-term systems: The trailing-stop version of the Harris 3L-R pattern
variation
This and the next strategy are two good examples of when things don’t work out
as intended and it isn’t obvious what’s causing the problem. Tables 28.9 and 28.10
show that the trailing-stop version of the Harris 3L-R pattern variation system only
managed to produce an average annual return of 1.79 percent when traded on both
the Dow and the NASDAQ stocks, at a fictive risk of 2 and 0.5 percent, respectively. These tables can be compared to Tables 14.6, 20.8, and 21.5.
TAB LE
28.9
Strategy 5 Results
Profitability
End. Equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Trade statistics
1,185,639
19
1.79
No. trades:
Avg. trade ($):
Avg. DIT:
5,215
36
2.9
1.04
Avg. win/loss ($):
1,820
35
51
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
24,178
Max DD (%):
24.1
Tr./Mark./Year:
Longest flat (M):
28.3
Tr./Month:
(1,361)
(16,016)
41.6
99
10.1
9.1
45.3
CHAPTER 28
TAB LE
357
28.10
Cumulative
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–8.00%
2.97%
–20.61%
8.06%
–16.37%
15.50%
–4.10%
22.43%
–1.72%
28.89%
15.58%
–16.34%
24.08%
–21.97%
32.20%
–16.37%
44.00%
–5.05%
57.38%
–4.73%
7.83%
11.95%
11.82%
13.00%
15.46%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–8.00%
2.97%
–10.90%
3.95%
–5.79%
4.92%
–1.04%
5.19%
–0.35%
5.21%
15.58%
–16.34%
7.83%
11.39%
–11.66%
5.81%
9.75%
–5.79%
3.79%
9.55%
–1.29%
3.10%
9.49%
–0.96%
2.92%
Best:
Worst:
St. dev:
Best:
Worst:
St. dev:
When looking at the equity and drawdown charts, some interesting observations can be made. It’s obvious that the strategy has not coped well at all with the
current bear market. However, the entire testing period leading up to the current
downturn has a very smooth and steady equity growth, with only a handful of
drawdowns surpassing 5 percent. (The equity and drawdown charts are not shown
for this strategy, but they are very similar in look and feel to those for Strategy 6.)
One reason for the poor result could be that the strategy is functioning so
badly in the current bear market that it forces us to keep the risk per trade down.
Had it functioned a little better in the bear market, it is possible that we could have
traded it a bit more aggressively and thereby also increased the profit potential during the bull market of the 1990s. The low drawdown numbers for this period indicate that we could take on plenty more risk per trade without taking the drawdowns
to such high levels as 15 to 20 percent. This is probably especially true for the NASDAQ stocks, which we are trading very conservatively using the current settings.
Another reason for the poor results could be that we are not in as many positions as we should be, given our assumptions about the relationships between the
stop-loss distance, the average trade length, and the money management point. We
aimed at being in approximately 10 open positions at any one time; with 45 trades
per month, and the average trade length being close to three days, the strategy is
seldom in more than six positions at the same time.
To come to grips with this, we need to either place all the stops and exits further away from the entry, both in terms of price and time, so that we spend more
time in a trade, or place the money management point closer to the entry so that
we increase the profit potential of each trade using the current stop and exit settings. The closer the MMP, the larger the position must be in terms of number of
358
shares traded, and the more shares traded, the larger the profit and loss potential in
any individual trade.
Most likely, we need to look into a combination of the two solutions. With the
trades being too short, the profit potential for any individual trade might be too
small to make up for the costs of trading to make any of these strategies worthwhile.
STRATEGY 6
■
■
■
Short-term systems: The stop-loss version of the expert exits system
The conclusions we came to for Strategy 5 also can be made for Strategy 6,
except the results are a tad better for this strategy, with an average annual return
of 4.86 percent, a maximum drawdown of 17.5 percent, and a Sharpe ratio of 0.53
(0.23 for Strategy 5). In this case, the fictive risk is set to 1 percent per trade,
which results in a maximum equity of close to $1.9 million (see Figure 28.8) and
only one drawdown surpassing 3 percent (see Figure 28.9) before the bear market
sets in.
The important lesson to be learned from these two strategies is that there is
no guarantee that the system will work as intended, even after we have gone
FIGURE
28.8
CHAPTER 28
FIGURE
359
28.9
through all the elaborate steps of testing and analysis. I know it can be tempting to
go ahead and trade them anyway, as a sort of reward for all the hard work, but if
they don’t work, they don’t work and should be scrapped—or at least taken apart,
so that their parts can be reused in other systems and strategies. As we will soon
see, sometimes when reusing parts from old systems, we strike gold that makes all
the hard work worthwhile.
STRATEGY 7
■
■
■
Long-term filter: Relative-strength bands
Short-term systems: The stop-loss versions of the hybrid system No. 1 and
Meander system, v.1.0, and the trailing-stop version of the volume-weighted average system
With the relative-strength bands and the rotation as the filters, we were only
testing 10 markets from each index category per system. Thus, because these
filters were true relative-strength filters, we were comparing the stock we
intend to trade directly with a set of other stocks instead of a comparable index;
this made the testing procedure rather cumbersome and time consuming. So,
for each filter and with 20 stocks to test, we can apply three systems to each
360
market, for a total of 60 symacs, which is the maximum our spreadsheet can
handle.
In this test, we apply the relative-strength bands as the filter, the stop-loss
versions of the hybrid system No. 1 and the Meander system v.1.0, and the trailing-stop version of the volume-weighted average system to 10 stocks each from
the Dow and NASDAQ groups, risking 2.5 percent per trade in all trades. The
results can be seen in Tables 28.11 and 28.12, and Figures 28.10 and 28.11.
With an average annual return of 10.8 percent, a maximum drawdown of 25
percent, and a Sharpe ratio of 0.73, we have a strategy that is doing much better
than a buy-and-hold strategy on any of the indexes (see Table 28.1). Another positive is the high percentage of both winning months and winning trades.
Unfortunately however, Figures 28.10 and 28.11 show that this strategy too
is in the midst of its worst historical drawdown, with no signs of forming a botTAB LE
28.11
Strategy 7 Results
Profitability
Trade statistics
End. Equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Max DD (%):
Longest flat (M):
TAB LE
2,673,676
167
10.81
1.15
62
64
25.3
13.0
No. trades:
Avg. trade ($):
Avg. DIT:
Avg. win/loss ($):
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
3,703
452
6,625
59,944
99
4.7
(6,398)
(54,385)
52.6
11.7
6.4
32.2
28.12
Profitability
End. Equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Trade statistics
2,084,306
108
No. trades:
Avg. trade ($):
7.96
1.12
Avg. DIT:
Avg. win/loss ($):
59
59
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Max DD (%):
20.9
Tr./Mark./Year:
Longest flat (M):
19.2
Tr./Month:
4,535
239
4,388
56,176
100
3.4
(3,836)
(42,637)
46.5
10.3
7.9
39.4
CHAPTER 28
FIGURE
28.10
FIGURE
28.11
361
362
tom. Again, this is most likely a consequence of the current bear market and the
fact that none of the systems forming the strategy looks to go short.
However, although the current drawdown is quite significant in size, remember that it is a function of how much we risk per trade, and that it doesn’t come anywhere near the drawdowns of the indexes. Aside from the last few drawdowns generated by the bear market, the maximum drawdown is only 10 percent, and judging
from Figure 28.11, the most common drawdown seems to be around 5 percent.
STRATEGY 8
■
■
■
Long-term filter: Relative-strength bands
Short-term systems: Same as for Strategy 7, plus the stop-loss versions of
the Harris 3L-R pattern variation and the expert exits system, and the trailing-stop version of the Harris 3L-R pattern variation
For this strategy, we continue to use the relative-strength bands as the filter, but
substitute the three systems trading the NASDAQ stocks with three more systems
trading the Dow stocks. Thus, we are now trading the same 10 Dow stocks with
six different versions of the systems we have worked with throughout the book. To
the systems used in the previous strategy, we have added the stop-loss versions of
FIGURE
28.12
CHAPTER 28
363
both the Harris 3L-R pattern variation and the expert exits system, and the trailing-stop version of the Harris 3L-R pattern variation.
With a fictive risk of 3 percent per trade for all system–market combinations,
the average annual return comes out to close to 8 percent, with a maximum drawdown of 21 percent. The Sharpe ratio comes out to 0.81. Although the average
annual return is slightly lower than that for a buy-and-hold strategy on the Dow
Jones index, a higher Sharpe ratio and a lower maximum drawdown make this
strategy a comparable alternative to the buy-and-hold (although it wouldn’t have
hurt if both the percentage of winning months and winning trades had been a tad
higher).
One way to increase the return—or at least the Sharpe ratio (in the form of
lower drawdowns)—would be to not trade the same 10 stocks with all systems.
Making sure all groups hold a different set of stocks would increase the diversification further and thereby also decrease the risk. Decreasing the risk would in turn
allow us to trade the system more aggressively, which would further increase the
returns. This would also increase the historical drawdowns somewhat, but judging
by Figure 28.12, the drawdowns leading up to the current bear market are very
modest. If we can keep the current drawdown under control, increasing the average drawdown wouldn’t do that much as long as we also can increase the return
and the Sharpe ratio.
STRATEGY 9
■
■
■
Long-term filter: Rotation
Short-term systems: The trailing-stop versions of the hybrid system No. 1,
Meander system v.1.0, and the volume-weighted average system
Markets: 10 Dow stocks, 10 NASDAQ stocks, for a total of 60 symacs
TAB LE
28.13
Strategy 9 Results
Profitability
End. Equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Trade statistics
2,706,109
171
10.95
No. trades:
Avg. trade ($):
Avg. DIT:
2,860
597
5.2
1.12
Avg. win/loss ($):
11,542
(10,471)
68
58
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
201,288
(129,841)
49.9
9.6
Max DD (%):
40.9
Tr./Mark./Year:
Longest flat (M):
20.8
Tr./Month:
99
5.0
24.9
364
Moving on to the last of our filters, the rotation, we start by testing it on both
groups of stocks, together with the trailing-stop versions of hybrid system No. 1,
Meander system v.1.0, and the volume-weighted average system, with the fictive
risk set to 5 percent for all trades.
Although the average annual return is a tad higher for this strategy than for
the previous one, if you only have these two strategies to choose from, this is not
the preferred alternative—at least not as it stands right now, without any short-selling possibilities or other markets complementing it on the short side.
This is evident when looking at the Sharpe ratio, which equals 0.5, and a
maximum drawdown in the current bear market of 41 percent. Again, both the percentage of winning months and winning trades could have been higher, although
there is nothing wrong with 58 percent winning months and close to 50 percent
winning trades.
Aside from the actual size of the current drawdown, the way this strategy has
handled the bear market also leaves a lot to wish for, when compared to many of
the other strategies. The fact that it hasn’t managed to set a new equity high over
the last several months indicates that it is much more dependent on the long-term
underlying trend than many of the other strategies.
However, as long as the trend is right, this strategy works very well, reaching a maximum equity peak of more than $4.5 million, with only one drawdown
FIGURE
28.13
CHAPTER 28
365
surpassing 15 percent on the way. But as soon as the bear market grabs hold of it,
the results are less tantalizing. Maybe the thing to do with this strategy would be
to put it aside for now and then use it as a complement to other strategies once the
long-term trend shows signs of having reversed itself?
STRATEGY 10
■
■
■
Long-term filter: Rotation
Short-term systems: Same as for Strategy 9, plus the stop-loss versions of
the Harris 3L-R pattern variation and the expert exits system, and the trailing-stop version of the expert exits system
Markets: 10 NASDAQ stocks, for a total of 60 symacs
Here’s another example of a very aggressively traded strategy. In this case, I substituted the systems trading Dow stocks with three more systems trading the NASDAQ stocks. The systems added are the stop-loss versions of the Harris 3L-R pattern variation and expert exits systems, and the trailing-stop version of the expert
exits system. All systems and markets were tested with the fictive risk set to 25
percent.
This time the percentage of winning months, at 49 percent, is definitely too
low. But looking at the equity curve, we can see that the reason is the long periods
of complete inactivity early on in the testing period. This occurs because a few of
the 10 stocks used in the testing weren’t trading at the time, which also explains
the exceptionally long flat period and slow equity growth over the first half of the
period. (I picked the stocks at random, so I had no way of controlling this.)
Excluding this period from the testing, the average annual return, which now
comes out to 16.6 percent, most likely would have been at least twice as high.
TAB LE
28.14
Strategy 10 Results
Profitability
End. equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Trade statistics
4,372,678
337
16.64
No. trades:
Avg. trade ($):
Avg. DIT:
1,377
2,449
3.2
1.15
Avg. win/loss ($):
36,194
(30,097)
70
49
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
727,346
(452,035)
47.2
3.1
Max DD (%):
40.9
Tr./Mark./Year:
Longest flat (M):
32.0
Tr./Month:
66
2.4
12.0
366
FIGURE
28.14
(Because of the compounding effect, making the same money over half the time
requires an average annual return for the shorter time period that is more than double the return of the longer period.)
Had it just so happened that the stocks used in the test were available for trading from the very beginning, most likely the results would have been much better
with both a higher average annual return and Sharpe ratio, which now comes out
to 0.36. I doubt, however, that we could have done that much about the latest 41
percent drawdown in the current bear market. Perhaps it wouldn’t have been quite
as severe, but judging from all the other strategies that use the NASDAQ stocks,
we still would have been in a deep drawdown, no matter which and how many
NASDAQ stocks we traded. If anything, perhaps one or two more equity highs
would have broken apart the current flat period into several shorter periods.
STRATEGY 11
■
■
■
Long-term filters: Either the relative-strength bands or the rotation, working independently from one another
Short-term systems: Both versions of hybrid system No. 1, Meander system v.1.0, and the volume-weighted average system
CHAPTER 28
367
For the last two strategies I used two filters working parallel to each other, so that
either one of them can open up a trading opportunity for any of the short-term systems. The first strategy trades 10 Dow stocks for a total of 60 system–market combinations, all traded with a fictive risk of 3 percent.
Tables 28.15 and 28.16 show the result for this strategy. With an average
annual return of 7.42 percent, a Sharpe ratio of 0.59, a maximum drawdown of 34
percent, and a longest flat time of 20 months, these numbers come very close to
those of a buy-and-hold strategy on the Dow. However, one major difference
between a trading strategy like this and a buy-and-hold strategy is that in a buyand-hold strategy you need to be in all the stocks all the time, tying up 100 perTAB LE
28.15
Strategy 11 Results
Profitability
Trade statistics
End. equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Max DD (%):
Longest flat (M):
TAB LE
1,985,057
99
7.42
1.10
67
62
34.2
20.0
No. trades:
Avg. trade ($):
Avg. DIT:
Avg. win/loss ($):
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
4,730
78,548
100
4,184
235
5.1
(4,487)
(36,127)
49.9
13.8
7.3
36.4
28.16
Strategy 11 Results
Cumulative
12 months
24 months
36 months
Most recent:
48 months
60 months
–19.86%
–25.77%
–21.25%
0.37%
19.36%
Average:
Best:
10.22%
40.68%
25.88%
59.65%
45.88%
84.98%
67.86%
112.35%
92.96%
151.78%
Worst:
St. dev:
–24.93%
12.67%
–25.77%
18.45%
–21.25%
23.36%
–3.97%
28.82%
11.21%
30.64%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–19.86%
10.22%
–13.85%
12.20%
–7.65%
13.41%
0.09%
13.83%
3.60%
14.05%
Best:
Worst:
40.68%
–24.93%
26.35%
–13.85%
22.76%
–7.65%
20.72%
–1.01%
20.28%
2.15%
St. dev:
12.67%
8.84%
7.25%
6.54%
5.49%
368
cent of your equity at all times. The more money you need to tie up to reach a certain return, the riskier the strategy, because the more you stand to lose if things go
severely against you.
For this strategy, you only need to tie up 67 percent of your capital on average, and only be in each stock 13 percent of the time. Thus, you will have plenty of
available capital left for other investment or trading endeavors, which will increase
your total return even further, while you also achieve additional diversification.
Also, if the strategy is any good, the time spent in the market for any individual stock should be high-quality time, meaning you should only be in a trade when
you have the highest likelihood for success, or at least the lowest likelihood for failure. This too, makes a mechanical trading strategy less risky than staying in a buyand-hold, where you have to stay in the market, come hell or high water. This should
show up in the number of profitable months, which should be higher for the mechanical strategy than for the buy-and-hold strategy and preferably also closer to 70 than
60 percent—although this is not the case this time (compare with Table 28.1).
As for the drawdowns, Figures 28.15 and 28.16 once again tell us that the
strategy worked very well up until the latest bear market, at which time it started
to give back previously made profits. To come to grips with this, complement this
strategy with one for the short side and possibly also decrease the amount risked
per trade when all signs indicate we’re in a bear market.
FIGURE
28.15
CHAPTER 28
FIGURE
369
28.16
STRATEGY 12
■
■
■
Long-term filters: Either the relative-strength bands or the rotation, working independently of one another
Short-term systems: Both versions of hybrid system No. 1, Meander system v.1.0, and the volume-weighted average system
Markets: 10 NASDAQ stocks, for a total of 60 symacs
The very last strategy is the same as the previous one, except 10 Dow stocks are
replaced by 10 NASDAQ stocks. In this case, the average annual return comes out
to 12.24 percent, the Sharpe ratio to 0.34, the maximum drawdown to 36 percent,
and the longest flat time to 21.5 months.
Comparing these numbers to the buy-and-hold stats for the NASDAQ 100 in
Table 28.1, we can see that this strategy is doing much better, not only on an
absolute return basis, but also on a relative basis, than the previous strategy did
when compared to the buy-and-hold stats for the Dow. In this case, the only number that does not hold up is the percentage of profitable months, which, at a mere
53 percent, is not only lower than the 56 percent for the buy-and-hold strategy, but
also much lower than we would like it to be.
Two good things are that the drawdown is much lower and the flat time is
much shorter than for the buy-and-hold strategy. Although the latest bear market
370
has taken its toll on all the systems, as with all the strategies tested on the NASDAQ stocks, it seems as if the volatility of the stocks still manages to produce
good-enough trading opportunities to set a new equity high every now and then.
Also, note in Figure 28.17 that the longest flat period for this strategy came prior
to the bull-market run in the late 1990s.
Looking at Figure 28.18, it also is obvious that this strategy didn’t do all that
well for the first half of the tested period. Looking only at the second half of the
tested period, the average annual return should be at least twice as high as the average return for the entire period.
We already know that one major reason for this is that a few of the stocks in
this test actually didn’t start trading until late in the 1990s. However, looking at
Figure 28.18, unfortunately, it also is fair to say that the entire growth in the equity comes from one lucky period, the bull market run in the late 1990s. Of course,
this is not a good thing, but we should take a closer look at Table 28.18 to see what
we can learn from it.
If you compare the average annual return in Table 28.17 with the 12-month
rolling return in Table 28.18, you’ll see that the 12-month rolling return is much
higher. How can this be?
The result from one exceptionally good period will not only influence the
result for the year it happened, but also for the 12 rolling periods following it. To
take it from the beginning:
FIGURE
28.17
CHAPTER 28
FIGURE
371
28.18
To take $1,000,000 to $3,024,987 over 9.58 years, which is the exact length
of the testing period, we need a constant compounded equity growth of 0.9588
percent per month. But as soon as we have both winning and losing periods, after
a losing month, it takes a relatively larger winning month just to break even. This
means that the average arithmetic return needs to be slightly larger that the constant compounded return. In this case, it comes out to 1.0878 percent per month.
TAB LE
28.17
Strategy 12 Results
Profitability
End. Equity ($):
Total return (%):
Profit factor:
Avg. tied cap (%):
Win. Months (%):
Drawdown
Trade statistics
3,024,987
202
12.24
No. trades:
Avg. trade ($):
Avg. DIT:
2,314
875
4.8
1.17
Avg. win/loss ($):
11,908
(11,461)
56
53
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
94,233
(76,148)
52.2
7.5
Max DD (%):
36.2
Tr./Mark./Year:
Longest flat (M):
21.5
Tr./Month:
84
4.0
20.1
372
TAB LE
28.18
Strategy 12 Rolling Time-window Analysis
Cumulative
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–24.38%
20.51%
–25.40%
54.51%
27.05%
96.31%
132.20%
129.07%
153.45%
167.01%
Best:
Worst:
145.21%
–28.25%
217.60%
–25.40%
255.75%
4.76%
281.16%
13.21%
289.60%
19.19%
St. dev:
35.57%
69.90%
89.81%
95.42%
94.23%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
–24.38%
20.51%
–13.63%
24.30%
8.31%
25.21%
23.44%
23.02%
20.44%
21.70%
Best:
Worst:
St. dev:
145.21%
–28.25%
35.57%
78.21%
–13.63%
30.35%
52.66%
1.56%
23.82%
39.73%
3.15%
18.23%
31.26%
3.57%
14.20%
For example, if you lose 10 percent of your capital one period, you will need
to make 11.1 percent the next just to break even, which would make the constant
period return zero, but the average period return to 0.55 percent [(10 11.1) /
2]. The larger the price swings, the greater the differences between the constant
period return and the average period return. For example, if you first lose 50 percent one period and gain 100 percent the next, to get back to the break-even point,
the constant period return will still be zero, but the average period return will be
25 percent [(-50 100) / 2].
Furthermore, a constant monthly growth rate of 0.9588 percent would result
in a 12.13 percent growth rate for any 12-month period. But with a varying period return, a large return one month will influence the rolling 12-month return for
the next 12 rolling periods, which in turn will make the average 12-month rolling
return look higher than the average compounded yearly return. The larger, faster,
and more frequent the swings in the equity, the larger the average 12-month rolling
return will be, compared to the average compounded yearly return.
In this case, we have one exceptionally fast period of equity growth during
1999, one steep drawdown in 2001, followed by another fast run up (not ending in
a new equity high), and yet another fast decline. Consequently, a 12-month rolling
return much larger than the average annual return is a good indication that there
have been large swings in the equity curve and that the final result might be the
result of one large swing in the equity, which is more or less the result of this strategy. Knowing this, you can use this information when comparing several strategies
or fund managers with each other and avoid those that simply seemed to luck out
over a short period of time.
CHAPTER 28
373
Other than that, rolling time-window analysis can come in handy when comparing the performance of different strategies over several overlapping periods. It
also helps us keep things in perspective during exceptionally good or bad times.
For example, despite the fact that we currently are in a 36 percent drawdown and
have lost more than 24 percent of our equity over the last 12 months, over the last
five years (60 months) we’re still up 153 percent, which translates to a growth rate
of 20.44 percent per year. This isn’t bad at all by any standard and much better than
the 3.6 percent yearly produced by the same strategy applied to the Dow stocks.
Also, note that this version of the strategy has no losing 36-month period,
which is reassuring to know during the bad times. That is, even during the slowest
and dullest times, the NASDAQ version of the strategy has managed to produce a
new equity high at least every 36 months, which is not the case with the Dow version. Naturally, the shorter the necessary time window to produce a profit, the better off you are.
To be fair, however, no losing period longer than 36 months isn’t all that good
either. Ideally, there should be no losing periods longer than 24 months. The closest we get to that in this book are with strategies 1 and 2. Table 28.5 shows that
Strategy 2 only loses (at most) 0.54 percent over two years. Table 28.3 shows that
Strategy 1 loses (at most) 15.84 percent over two years, but to compensate, it also
has made at least 10.40 percent a year for any rolling three-year period.
However, when looking at these numbers, we must keep in mind that we’re
looking at historical or back-tested results. To get a better feel for what we can expect
in the future, we must look at the standard deviations and compare them to the average period return. For example, Table 28.18 tells us that the average 12-month rolling
return is 20.51 percent and the standard deviation is 35.57 percent. Thus, 68 percent
of all 12-month returns should fall somewhere in the interval 15.05 to 56.08 percent (20.51 35.57), which means that only 16 percent of all rolling returns should
come in below –15.05 percent [(1 0.68) / 2]. Because this is the case with the most
recent return of –24.38, we have reason to believe that this is not a typical result for
this strategy and that we therefore should do better in the upcoming periods.
For Strategy 11, we have reason to be even more optimistic about the future.
Because Table 28.16 tells us that the average period return is 10.22 and the standard deviation is 12.67, we can estimate that 95 percent of all period returns will
fall somewhere in the interval 15.12 to 35.56 percent (10.22 12.67 * 2).
Because the most recent return falls outside this interval, it is even less likely to
be a good estimate of what is to come. In this case, the most recent return belongs
to a group of only 2.5 percent [(1 0.95) / 2] of all returns that are as bad as this
one. However, there are no guarantees. The next period return can still be all over
the place, with a very high likelihood of being negative.
Looking at the rolling time-window analysis helps us get a feel for how reliable and stable the strategy or the fund manager is and how likely it is that either
one will continue to produce the same results in the future as it has in the past.
374
THE COUNTERPUNCH STOCK SYSTEM
It’s important to remember that just because you have taken a system through all the
elaborate steps of testing, you don’t have to trade it—although it might be tempting
to do so just to make all the hard work worthwhile. If a system isn’t good enough to
be traded, it isn’t good enough to be traded, and not all ideas will turn out to be profitable enough in the end, no matter how clever they seemed when conceived.
However, just because you shouldn’t trade a system or strategy as it stands
here and now, doesn’t mean that all its parts are useless. Sometimes it may be a
good idea to combine various sets of old entry and exit techniques, with or without filters, and test them as new strategies. After you have tested and developed a
few systems and strategies according to these guidelines, you probably will have
a basket of unused strategy combinations to choose from.
As a bonus for ending this book, and just to show you that there never is such
a thing as a bad idea and all ideas are worth saving, let me show you the results for
the last system I developed for Active Trader.
The entry idea is from a system I created for Trading Systems That Work to
be traded on the S&P 500 futures market, but without its original filter. The exit
rules are from a series of articles I wrote for Active Trader and published over the
period March through June 2002. Neither the entry nor the exits have ever been
applied to these stocks before.
FIGURE
28.19
The equity curve for the counterpunch strategy.
CHAPTER 28
TAB LE
375
28.19
The Results for the Counterpunch Strategy
Profitability
Trade statistics
End. equity ($):
Total return (%):
4,868,697
387
Profit factor:
Avg. tied cap (%):
Win. months (%):
Drawdown
Max DD (%):
Longest flat (M):
TAB LE
No. trades:
Avg. trade ($):
17.96
1.24
Avg. DIT:
Avg. win/loss ($):
57
72
Lrg. win/loss ($):
Win. trades (%):
TIM (%):
Tr./Mark./Year:
Tr./Month:
7.3
6.1
18,893
205
2,870
26,242
100
2.3
(1,343)
(22,755)
38.4
28.0
32.9
164.3
28.20
The Rolling Time-window Analysis for the Counterpunch Strategy
Cumulative
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
Best:
Worst:
St. dev:
11.45%
17.80%
47.83%
4.23%
10.14%
37.60%
41.09%
82.37%
10.48%
19.19%
69.74%
69.79%
128.21%
34.46%
28.64%
144.87%
102.36%
153.66%
47.01%
37.53%
180.09%
137.81%
183.47%
63.91%
39.14%
Annualized
12 months
24 months
36 months
48 months
60 months
Most recent:
Average:
Best:
Worst:
St. dev:
11.45%
17.80%
47.83%
4.23%
10.14%
17.30%
18.78%
35.04%
5.11%
9.17%
19.29%
19.30%
31.66%
10.37%
8.76%
25.09%
19.27%
26.20%
10.11%
8.29%
22.87%
18.92%
23.17%
10.39%
6.83%
Originally featured in November 2002, this countertrend system looks for
long positions when everyone else is selling short and vice versa. It is based on the
premise that no trend lasts forever, and the longer one lasts, the more likely a
short-term reversal will occur.
The system will take a position against the prevailing intermediate-term
trend if a price has moved in the same direction for two weeks in a row and for two
days in a row in the most recent week. The reversal that follows won’t necessarily
be of the same magnitude as the trend preceding it, but many times it will be large
enough to generate a steady profit for the system.
376
This system trades both sides of the market the same way, thus short trades
made during a prolonged uptrend will probably not fare as well as those made
from the long side. However, the counter to this is that when the long-term trend
is down, as it has been the last couple of years, the system is well prepared to profit from the short side.
SUGGESTED MARKETS
Stocks, stock-index futures, and stock-index shares.
RULES
Go long tomorrow on the open if a) today’s close is below both yesterday’s close and
the close of the previous week, b) yesterday’s close is below the previous day’s close
and, c) the close of the previous week is below the close of the week before that.
Exit first half of position with a loss if the trade goes against you by 1 percent.
Exit first half of position with a profit if the trade goes your way by 4 percent.
Exit second half with a profit or loss if the trade moves 1.6 percent away
from your maximum open profit (i.e., trail a stop 1.6 percent below the high of the
trade).
Exit second half with a profit if the trade goes your way by 4.5 percent.
Exit the entire position after eight days in the trade.
Reverse the rules for short trades.
MONEY MANAGEMENT
Risk 2.5 percent of available equity per stock. The number of shares to trade (ST)
is determined by the following formula:
ST AC * PR / TR
Where:
PR Percent risked ( fictive f in the rest of the book)
TR Four times the true range for the day preceding the entry
TEST PERIOD
January 1993 to July 2002.
CHAPTER 28
377
TEST DATA
Daily prices for the 30 stocks making up the Dow Jones Industrial Average. A total
of $10 slippage and commission deducted per trade.
STARTING EQUITY
$1 million (nominal).
SYSTEM ANALYSIS
The results of this system are amazing by any standard. The average annual return
is almost 18 percent, which is close to twice the buy-and-hold return on the Dow
Jones over the same period. The largest drawdown is 7.3 percent, while the longest
flat time is six months. For a buy-and-hold strategy on the DJIA, which performed
far better than the S&P 500 and NASDAQ indices, those numbers were 36 percent
and 30 months, respectively. Also, this system is completely unoptimized, which
proves two things:
First, a system doesn’t have to be complicated to be profitable. Second, the
fewer the rules and the easier the system is to understand, the more likely it will
continue to hold up in the future. Because the stock market does not behave the
same in a downtrend as it does in an uptrend, to improve this system, the long and
short trades could be separated and the entry and exit rules tailored to each.
By either removing a few long-entry rules or adding a few short-entry rules,
the system’s performance would likely improve and make it relatively easier to
enter on the long side.
Likewise, it would probably help to make it relatively easier to exit the short
trades by tightening the short-trade exits or loosening the long-trade exits.
However, why tinker? This system is already delivering a risk-adjusted return
well above that of the buy-and-hold strategy.
CHAPTER
29
Consistent Strategies
T
he fourth and final part of the book started by discussing the paradox between a
near-random market and a profitable but seemingly random system. With the markets being as close to random as they are, a good trading system must make the
most out of the nonrandom periods, while keeping you in the game during the random periods. The more nonrandom information we make use of, the less useful
information is left, up to the point where only random market noise is left. The
more random noise is left in relation to unused information, the closer to randomly our system will behave.
Therefore, as long as the system has a decent mathematical expectancy, the
more nonrandom information the system makes use of, the more difficult it will
be to predict the outcome of any of its trades. However, not knowing if the outcome of the next trade will be a winner or a loser makes it all the more important
to adhere to your stops and exit signals to keep all the trades as similar to each
other as possible. If you follow a consistent trading approach, the more trades that
conform to a certain profit–loss size and trade length, the more you can chalk up
your success to skill instead of luck.
Furthermore, although you can’t be sure of the outcome of the next trade, by
adhering to your stops and exits, you can decide what the maximum loss will be
by always risking the same relative amount in relation to the available capital on
each trade. One way to calculate the proper amount to risk is to use the Kelly formula. Once the Kelly value (K) is determined, you can determine how many shares
to buy and how much capital must go towards this trade. The larger the K, the more
money you can put into one trade; the smaller the K, the less money you should
put into one trade. Also, the tighter the stop loss, the more of your capital you need
379
380
to put into one trade; the wider the stop loss, the less capital you need to put into
one trade.
A good trader also tries to balance the steepness of the equity curve with its
smoothness, so that the steeper the better and the smoother the better. The more you
risk, the more erratic the equity curve and the riskier the trading in general terms.
The major flaw with the Kelly formula is that it assumes two outcomes
only—a winner of a certain magnitude and a loser of a certain magnitude.
Therefore, it is better to use the formula for optimal f, as popularized by Ralph
Vince.
In Ralph Vince’s original version of the formula, f depends on the worst historical loser, because we’re implicitly assuming that one reason to trade this system is that its largest historical loser is within the limits for what we can tolerate,
given the profit potential of the system.
To make a long story short, calculating the ending equity, which Ralph Vince
dubbed terminal wealth relative (TWR), is done using the following formula:
TWR GMN HPR1 * HPR2 * HPR3 * … * HPRi
Where:
GM (APM2 SD2)(N/2)
HPRn 1 f * (Profitn / WCS)
TWR Terminal wealth relative, expressed as the percentage compounded
return over a trading sequence
GM The geometric mean
N Number of trades
APM The average profit multiplier, calculated as the average percentage
profit per trade divided by 100, plus one
SD Standard deviation of all trades, measured in percentage terms
HPRn The holding period return for trade n, expressed as a percentage of
your total equity going into the trade
f The fixed fraction of your capital to risk in all trades
Profitn The profit or loss from trade n in dollars on a constant-shares
invested basis
WCS The historical worst-case scenario in dollars on a constant-shares
invested basis (expressed as a positive number)
Thus, given the largest historical loser, by altering f we can alter the size of
the profit or loss of any individual trade (HPRn) and consequently alter the TWR.
However, from the formula it also follows that TWR depends on how large the
average trade is in relation to the outcome of all trades (the larger the better) and
the number of trades (the more trades the better).
CHAPTER 29 Consistent Strategies
381
To end up with a positive TWR, we must make sure APM is larger than SD.
If we can achieve this, the end result for TWR will only be a function of f (the fraction of available equity to risk) and N (the total number of trades).
However, if we ever were to encounter a loss of the same size as the worst
historical loser, the loss for that trade also will equal f. Thus, the higher the systems profit-generating potential, and the higher the f, the more you stand to lose
in one single trade. Therefore, it’s better to replace the worst historical loser with
the stop-loss level for each individual trade for all trades. By doing so, the worstcase scenario will be based on a reasonable amount that you’re willing to risk for
each trade, instead of a terrifying amount that you were willing to tolerate in the
past, but would rather not encounter again.
However, the dilemma for the short-term trader is that short-term trading
usually means a low average profit per trade and the use of tight stop losses that
makes sense in relation to the estimated and desired average trade length. But the
tighter the stops on a one-share basis, the fewer trades he can be in simultaneously for any given f.
To work around this, separate the stop loss (SL) from the money management point (MMP). Originally, we assumed SL to be equal to MMP, but by separating the two and placing MMP further away from the entry price, we can lower
the number of shares to buy and the amount of our capital tied up in each trade.
As a consequence of this, the f used to calculate the number of shares to buy won’t
represent the true fraction risked of the available equity, but rather just a fictive
fraction to feed the formula:
ST (AC * ffict) / MMP
Where:
ST Shares to trade
MMP Money management point in distance from the entry price, to calculate the number of shares to trade
ffict Fictive fraction of capital to risk to calculate the number of shares to
trade
To calculate the actual amount risked in each trade, we can use the following
formula:
f = ffict * (SL / MMP)
Where:
SL Stop loss in distance from entry price
To figure out how many positions we can be in simultaneously, we only need
to divide MMP by ffict, or, if we already know how many positions we would like
382
to be in, we can calculate how far away from the entry price we need to place MMP
to make that possible by dividing the desired number of positions by ffict. This will
place MMP a fixed distance away from the entry price, but by letting the distance
for MMP vary around a desired average distance, we can vary the number of maximum positions with the behavior of the markets.
For example, if the volatility is high, we can place MMP further away from
the entry price than the desired average distance and thereby make each position
smaller. This makes room for more open positions and better diversification during times of turmoil, and vice versa. At the same time, a dynamic stop loss will
keep us from getting stopped out too frequently during times of turmoil, while it
will stick closer to the price of the stock in calmer times, when our positions are
larger.
CONCLUSION
Once we understood the process behind the DRMM, we were able to build a basic
spreadsheet for all the necessary calculations. With the help of this spreadsheet,
you can test a few system–market combinations traded within one portfolio using
the same account equity. We also took a closer look at a more professional spreadsheet and how it compared to a Web-based evaluation of the real-time trading
records of professional fund managers and CTAs.
With the help of the professional spreadsheet, we ended our research by taking a look at a few combinations of the systems and filters we worked with
throughout the book. By adding the money management and trading all the system–market combinations using a shared account equity, we shifted the focus from
the individual system to the complete strategy.
For most of the strategies, we tried to find the fictive f to risk per trade that
gave us an equity curve that was as smooth as possible in relation to the growth
rate. It’s important to note that nothing forces you to trade the exact optimal f for
the highest growth rate. Many times this may still be perceived as too risky. The
important thing is to not take any unnecessary risk by trading above the optimal f,
when the goal is to decrease the risk by optisizing on any other variable.
The first two strategies produced very good and low-risk results, although
the current bear market lowered the performance somewhat over the last several
months. The conclusion is that the meander indicator does a very good job in finding high-probability trading opportunities with high profit potentials.
Comparing Strategies 3 and 1, it’s easy to see that Strategy 3 didn’t come
anywhere close to the performance of Strategy 1. Even so, it still outperforms a
benchmark buy-and-hold strategy and could probably be trusted for real-time trading if combined with a system for trading the short side. Strategy 4 was optisized
on the maximum equity growth, rather than the Sharpe ratio and the smoothness
of the equity curve, which resulted in an average annual return of 32.5 percent.
CHAPTER 29 Consistent Strategies
383
Strategies 5 and 6 used the trailing-stop version of the Harris 3L-R pattern
variation and the stop-loss version of the expert exits systems. The results from
these two strategies were not satisfactory, probably because the systems turned out
to be too short term for our purposes. When a system is “too” short-term, with a
low risk–reward relationship, the profits won’t make up for the costs of trading
with slippage and commission included in the calculations. In this case, we probably also need to rebalance the distance between the entry price and the money
management point, and the distance between the entry price and the stop loss, to
optimize the number of positions we can be in simultaneously.
Strategy 7 produced satisfactory results, although the current bear market
once again forced the strategy into a new maximum drawdown. For Strategy 8, the
results could not be considered satisfactory. It is apparent that the shorter-term
systems—the Harris 3L-R pattern variation and the expert exits system—do not
work as intended.
Strategy 9 produced satisfactory results, despite a rather steep recent drawdown. Substituting the 10 Dow stocks in Strategy 9 with the same short-term systems as in Strategy 8 resulted in very choppy results for Strategy 10. Although the
profit potential is there, it is doubtful a strategy like this should be trusted for realtime trading—at least not when traded on only a handful of markets.
The last two strategies used a combination of the relative-strength bands and
the rotation filters. For Strategy 11, this resulted in a smooth and steady initial equity growth that again was weighted down by a larger than tolerable drawdown over
the last few years. For Strategy 12, the results were too choppy and the profits too
dependent on the bull-market run of the late 1990s. As was the case for Strategy 10,
it is doubtful a strategy like this should be trusted for real-time trading.
Looking through the overall results, three things come to mind. Number one
is that the shorter-term systems, the Harris 3L-R pattern variation and the expert
exits, did not work as intended, probably for two reasons: Reason one is that their
short trading horizons limit the profit potential. Reason two is that the money
management point probably is too close to the entry price, given the average stoploss distance, to allow us to be in an optimal number of positions at one time.
Reason two can be dealt with simply by shifting the MMP further away from the
entry price; reason one probably calls for a revision of the research surrounding
the stops and exits.
The second thing that comes to mind is that the relative-strength bands and
the rotation filters allowed us to test only 20 stocks, which limited our diversification possibilities. It is likely the risk-adjusted returns would have been higher for
Strategies 7 to 12 had we been able to test them on more stocks. Talking about the
filters, it’s also worth mentioning that several of the systems might have functioned better without them. I leave that for you to decide.
Last, but not least, most strategies probably should have done much better
trading the short side as well, despite the fact that it would have resulted in a slight
384
deterioration of performance over the bull market in the 1990s. Most likely this
would have been counterweighted by a better performance over the last few years
and perhaps also a smoother equity growth over the entire period. This would have
meant that we could have increased the performance even further by daring to risk
a bit more in each trade.
However, to be able to identify and do something about any of these reasons
for system failure, we need to do the research the right way from the very beginning. In Part 3, we learned how to come up with a set of stops and exits that should
work, on average equally as well on all markets.
Although we didn’t do it in this book, analyzing two variables at a time using
a surface chart also can be used for the entries. Here we instead used a set of
entries developed earlier for the Trading Systems lab pages for Active Trader magazine. In Part 2, we took the liberty to tinker around with them a bit, analyzing the
results from the changes using normalized results.
To work with normalized results, we must make sure that the data are correct, which testing variables are the most important to look at, and what type of
results to look for. Without knowing this, there is no way we can isolate any type
of problem or error, no matter where it occurs during the testing process. These
concepts were covered in Part 1, and thus we have come full circle.
INDEX
Note: Boldface numbers indicate illustrations.
Active Trader magazine, 4–5, 10, 55, 58, 65,
79, 80, 81, 84, 85, 95, 113, 123, 137,
155, 163, 173, 176, 185, 188, 220, 255,
296, 343, 374, 375
adding exits, 219–254
average profit per trade, 16–20, 17, 18, 19
average true range method, stops and,
211–212
average volume (AV), volume-weighted
average system and, 153
average winners and losers in, 20–22
back-adjustment method for splicing
contracts, 71–75, 72, 73, 74
Barclays Group, The, 329
benchmark indices, combined money market
strategies, 344–345, 345
Black Scholes evaluation, 5
Bollinger bands, 81, 123–124
Bradford-Raschke, Linda, 79–80
calculations in systems, number of, 188–189
Campaign Trading, 65
central limit theorem, profit calculation and,
25–28
Chebychef’s theorem, profit calculation and,
31
Citigroup traded using Harris 3L-R pattern
variation system, 170
closed trade drawdown (CTD), 63–65
code (See TradeStation code)
combined money market strategies, 343–377
benchmark indices for, 344–345, 345
counterpunch stock system in, 374–375,
374, 375
filters in, 344
hybrid system No. 1 in, 366–369, 367,
368, 369, 369–374, 370, 371, 372
meander system in, 366–369, 367, 368,
369, 369–374, 370, 371, 372
optimal f and, 343
relative strength bands as filter in,
359–374, 360–372
combined money market strategies (continued)
rotation filter in, 363–374, 363–371
RS system No. 1 as filter in, 344,
345–359, 346–359
Sharpe ratio and, 343
stocks used in, 344
stop-loss version of expert exits in,
362–363, 362, 365–366, 365, 366
stop-loss version of meander system in,
359–362, 360, 361
strategy 1, stop-loss version of meander
systems, 345–348, 346, 347, 349–351,
349, 350
strategy 2, trailing-stop version of
meander systems, 349–351, 349, 350
strategy 3 and 4, trailing-stop version of
volume-weighted average, 352–354,
352, 353, 354–356,
strategy 5, trailing-stop version of Harris
3L-R pattern variation, 356–358, 356,
357
strategy 6, stop-loss version of expert exits
in, 358–359, 358, 359
strategy 7, stop-loss version of hybrid
system No. 1 in, 359–362, 360, 361
strategy 8, stop-loss version of Harris
3L-R pattern variation in, 362–363,
362
strategy 9, trailing-stop version of hybrid
system No. 1, 363–365, 363, 364
strategy 10, stop-loss version of Harris
3L-R pattern variation in, 365–366,
365, 366
strategy 11, hybrid system, meander
system, volume-weighted average in,
366–369, 367, 368,
strategy vs. system in, 344
trailing-stop version of volume-weighted
average in, 359–362, 360, 361
trailing-stop version of expert exits in,
365–366, 365, 366
trailing-stop version of Harris 3L-R
pattern variation in, 362–363, 362
385
Index
386
combined money market strategies (continued)
trailing-stop version of meander system in,
363–365, 363, 364
trailing-stop version of volume-weighted
average system in, 363–365, 363, 364
volume-weighted average system in,
366–369, 367, 368, 369, 369–374, 370,
371, 372
commissions and fees, 12–13, 82
complicated systems, 188–189
consistency of system, 272–273, 379–384
costs of trading, 12–13, 82
counterpunch stock system
combined money market strategies,
374–375, 374, 375
money management in, 376
rules for, 376
starting equity for, 377
suggested markets for, 376
system analysis for, 377
test period/test data for, 377
cumulative monthly returns from spreadsheet,
336
curve fitting, 81–82
DeMark, Tom, 79
developing trading systems, 79–82
distribution of drawdowns from spreadsheet,
335
distribution of trades, 193–199, 192
leptokurtic, 26–28, 27
mean, median, and mode in, 25–28
platykurtic, 26–28, 27
profit calculation and, 25–28, 26, 27
profits and, 195–199, 195, 196, 197
stop loss and, 193–199, 193
Dow Jones Industrial Average stocks used in
analysis, 84–85
Dow Jones stocks used in analysis, 84–85
drawdown and losses, 57–65, 77–78,
278–279, 279
closed trade (CTD), 63–65
end trade (ETD), 63–65
equity compared to, 58–59, 59
market vs., 59–60
maximum adverse excursion (MAE) in, 65
maximum favorable excursion (MFE) in,
65
maximum of, 60–63
mean–median comparisons and, 60–63
percentage of profitable trades and, 62–63,
62
start trade (STD), 63–65
total equity (TED), 63–65, 64
drawdown and losses (continued)
types of, 63–65
underwater equity charts and, 59, 59
drawdown curve from spreadsheet, 334
dynamic ratio money management (DRMM),
85, 305–323, 307, 382
calculations in, for spreadsheet, 315–316
equity curve chart and, 318–319, 318, 322
formulas for, in spreadsheet, 316, 317–318
money management point (MMP) in,
306–323
optimal f and, 305–323, 307
sample spreadsheet using, 310–323,
311–314, 320, 321, 322
stop loss and, 306
underwater equity chart and, 319, 319, 323
EasyLanguage code (See also TradeStation
coding), 83–84
end of event exit, 204–205, 282, 283
end trade drawdown (ETD), 63–65
entry rules
Harris 3L-R pattern variation system and,
167–168
probability and percent of profitable
trades, 45–46
volume-weighted average system and, 156
equity, optimal f vs., 298–299, 299
equity curve chart and DRMM, 318–319,
318, 322
equity variation over trades, 277–278, 278
equity vs. drawdown, 58–59, 59
Etzkorn, Mark, 79
evaluating a system, 1–5
evaluating stops and exits, 281–285
evaluating system performance, 185–189
Excel spreadsheet of compiled trade results
(See also spreadsheet development),
273–274, 274
Excel, 10–11
exits, 189, 190, 201–206
adding, 219–254
end of event, 204–205, 282, 283
evaluation of, 281–285
expert exits and, 175–176, 178–182, 180,
181, 248–250
filters and, 284
245–248
limiting a loss using, 201–203, 282
meander system, 237–241
money better used elsewhere, 205–206,
283
profit targets as, 283
Index
387
exits (continued)
reasons for, 282
relative strength bands system and,
129–132, 132
rotation system and, 139, 140, 141
short vs. long in, 219
surface charts and, 283–284
taking a profit using, 203–204, 282
testing of, 284–285
types of, 282
variables to test in, 284
volume-weighted average system and, 156,
157, 241–245
expert exits, 80, 173–183
exit placement in, 220, 248–250
exit techniques in, 175–176
original rules for, 174
pros and cons of, 174–175
random number generator (RNG) and,
178, 179
relative strength bands filter use of in,
262–266, 262, 266, 269
revising and modifying, 175–182, 177
risk–reward ratio in, 176
short vs. long in, 174, 177–178, 177
signals generated by, 175–176, 176
stop loss and, 178–180, 180
stop-loss version of, 249, 249, 358–359,
358, 359, 362–363, 362, 365–366, 365,
366
time in market and, 174–175
TradeStation code for, 182–183
trailing stop in, 180–182, 180, 181
trailing-stop version of, 249, 250,
365–366, 365, 366
export code, TradeStation, 86–91
spreadsheet and, money management,
337–342
export function, 275
filters (See also systems as filters), 190,
255–269
combined money market strategies, 344
exits and, 284
systems as, 255–269
fixed fractional trading, 295–304
holding period return (HPR) in, 295–296,
380
optimal f in, 295–304
relative strength bands system and, 125
fixed fractional trading (continued)
terminal wealth relative (TWR) in,
295–304, 298, 299, 295
formulas for calculating profitable trades, 38
Freeburg, Nelson, 80
Futures magazine, 58, 65, 80, 255
futures market, 84
calculate number of contracts, code for,
11–12
quality data and, 71–75
splicing contracts in, 71–75, 72, 73, 74
geometric average, fixed fractional trading,
optimal f, and TWR in, 303–304
geometric mean (GM), fixed fractional
trading, optimal f, and TWR in,
303–304
Gramza, Dan, 80
Harris 3L-R pattern variation, 81, 163–172
entry rules in, 167–168
evaluation of, 188
length of trade in, 165–166
profit targets in, 166–167
profit–loss ratio in, 164–165
265–266, 265
revising and modifying, 165–171, 166,
170
risk–reward ratio in, 167–171, 167, 168,
169
rotation system filter use of in, 268–269,
268
RS system No. 1 filter use of in, 262
short vs. long in, 163, 165, 166
stop loss in, 166–167
stop-loss version of, 246–247, 246, 247,
362–363, 362, 365–366, 365, 366
trailing-stop version of, 247–248, 248,
356–358, 356, 357, 362–363, 362
trend filters in, 165
Harris, Michael, 79, 163, 188
Hedgefund, 247, 329
Hedgefund.net, 329
highest average volume (HAV), volumeweighted average system and, 153
holding period return (HPR), 295–296, 380
Index
388
hybrid system No. 1, 81, 97–103, 187–188
366–374, 367–372,
length in trade in, 100–102, 100, 101
on balance volume (OBV) in, 98
original rules for, 97–98
263–266, 263
risk–reward ratio and, 98–99
268
short vs. long term, 98–99, 101–102
slow trade stop in, 99–102, 101, 102
stop-loss version of, 226–233, 227, 233,
359–362, 360, 361
trailing-stop version of, 233–236,
234–236, 363–365, 363, 364
individual market summary, spreadsheet and,
336–337, 337
Institutional Advisory Services Group
(IASG), 325, 329, 330–333
International Traders Research, 329
Kelly formula, money management, 289–294,
292, 293
Kelly value (K), 379–380
kurtosis, 327–328
profit and, 23–25
Lane, David M., 22(f), 22
large export function, 276
length in trade
165–166
hybrid system No. 1 and, 100–102, 100, 101
RS system No. 1 and, 107–110
leptokurtic distributions, 26–28, 27
limiting a loss using an exit, 201–203, 282
lookback period, 108–109, 108, 186
meander system and, 117–118, 118
relative strength bands system and, 127,
127, 129, 130, 131
rotation system and, 140, 141–142, 142,
145–146
158–159, 158, 159
losers
distribution of trades and, 193–199, 192
winners and losers in a row, 38–43, 41, 42
losses (See drawdown and losses)
lowest average volume (LAV), volumeweighted average system and, 153
market vs. drawdown, 59–60
markets used in analysis, 84
max-length stop, 252, 253–254
maximum adverse excursion (MAE), 65
Maximum Adverse Excursion, 65
maximum favorable excursion (MFE), 65
mean, 25–28
drawdown and losses in, 60–63
mean square error, profit calculation and,
29–30
meander system, 80, 113–121
366–369, 367, 368, 369, 369–374, 370,
371, 372
evaluation of, 185
lookback period in, 117–118, 118
profit factors in, 114–115
264–266, 264
risk–reward ratio in, 115–116, 116
268
RS system No. 1 filter use of in, 260, 261
short vs. long term in, 118, 119, 120
slack period and time in market, 116–117,
117
stop loss in, 115
stop-loss version of, 237–240, 237–239,
345–351, 346–350, 359–362, 360, 361
349–351, 349, 350, 363–365, 363, 364
median, 25–28
drawdown and losses in, 60–63
Merck, volume-weighted average system and,
160
Meyers, Dennis, 55
Microsoft
expert exits and, 175–176, 176
Index
389
Microsoft (continued)
performance signals, 44, 45, 46
quality of data examples for, 67–78
trading data, 68, 69, 71
min-move stop, 252, 253
mode, standard deviation and, 25–28
money better used elsewhere exits, 205–206,
283
money management, 287–288
counterpunch stock system in, 376
dynamic ratio, 305–323, 307, 382
fixed fractional trading in, 295–304
Kelly formula for, 289–294, 292, 293
spreadsheet and, export code for, 337–342
money management point (MMP), 306–323,
337, 341, 381–382
money market strategies (See combined
money market strategies)
monthly distributions from spreadsheet, 335
moving average crossover system, 3
moving average slope (MAS), rotation system
and, 137
NASDAQ 100 stocks used in analysis, 84–85
NASDAQ stocks used in analysis, 84–85
net profit, 16
nonadjustment method for splicing contracts,
71–75, 72, 73, 74
normal distribution (See standard deviation)
number of shares traded, 8
on balance volume (OBV), 98, 258
optimal f, 295–304, 380–382
dynamic ratios and, 305–323, 307
spreadsheet and, 325
optimizing systems, 82
percentage of profitable trades, drawdown
and losses in, 62–63, 62
percentage vs. dollar amount changes, 4–5
percentage-based stops, 209–210, 250–251
percentages vs. dollar amounts, risk
calculation and, 51–55
percentages vs. normalized moves, 7–13
costs of trading and, 12–13
number of shares traded in, 8
profits in, 7–8, 10
short vs. long term trading systems and,
12–13
performance measures, 4–5
perpetual adjustment method for splicing
contracts, 71–75, 72, 73, 74
placing stops, 207–217
platykurtic distributions, 26–28, 27
point-based adjustment for splicing contracts,
71–75, 72, 73, 74
Portfolio Management Formulas, 295
previous bar VMA (PVMA), volumeweighted average system and, 153–154
probability and percent of profitable trades,
35–46
calculating profitable trades in, 35–43, 39,
40
entry rules and, 45–46
formulas for calculating profitable trades
in, 38
random number generator (RNG) and, 46,
46
trades vs. signals and, 43–46, 44
winners and losers in a row and, 38–43,
41, 42
product of all RSV lines (PRSV), 81
profit factors, filters and, 257–258
profit filters, 284
profit protector stop, 251, 253
profit target stop, 251, 253
profit targets, 283
profit–loss ratio, 95
164–165
profits, 7–8, 10, 15–33
average profit per trade in, 16–20, 17 18,
19
calculating profitable trades in, 35–43, 39,
40
central limit theorem and, 25–28
Chebychef’s theorem and, 31
distribution of trades and, 25–28, 26, 27,
195–199, 195, 196, 197
fixed fractional trading, optimal f, and
TWR in, 295–304
formulas for calculating profitable trades
in, 38
166–167
Kelly formula, money management,
289–294, 292, 293
kurtosis and, 23–25
mean square error in, 29–30
meander system and, 114–115
net profit in, 16
probability and, 35–46
profit–loss ratio, 95
Index
390
profits (continued)
quality data and, 76–78
127–128, 131–132
risk and risk adjusted return vs., 24–25
risk vs., 48–51
skew and, 23–25, 28
standard deviation and, 22–25
standard error and tests for, 28–30
successful trading system, chart of, 32
time in market vs., 31–33
trades vs. signals and, 43–46, 44
trimmean function in, 30–31
winners and losers in a row and, 38–43,
41, 42
quality data, 67–78
futures market example and, 71–75
profitability and, 76–78
ratio adjusted data (RAD) in, 75
random number generator (RNG)
expert exits and, 178, 179
probability and percent of profitable
trades, 46, 46
ratio adjusted data (RAD), 75
ratio adjusted method for splicing contracts,
71–75, 72, 73, 74
relative moving average (RMA), relative
strength bands system and, 123
relative strength bands, 81, 123–136, 220
Bollinger bands and, 123–124
filter use of, 262–266, 359–362, 360, 361,
366–374, 367–372
fixed fractional money management in,
125
lookback period in, 127, 127, 129, 130, 131
money market strategy using, 359–362,
360, 361
product of all RSV lines (PRSV) in, 123
profit factors in, 127–128, 131–132
pros and cons of, 125
relative moving average (RMA) in, 123
relative strength line (RSL) in, 123
risk–reward ratio in, 126–127, 126,
132–133
short vs. long term in, 130
standard deviation in, 128, 129, 131, 132
stops and exits for, 129–132, 132
relative strength bands (continued)
TradeStation code for, 133–136, 133
relative strength line (RSL), relative strength
bands system and, 123
relative value (RV), volume-weighted average
system and, 153
risk, 47–55
calculation of, 48–51
calculation of, in spreadsheet, 328–329
DRMM and, 309–323
TWR in, 295–304
Kelly formula, money management,
289–294, 292, 293
percentages vs. dollar amounts in, 51–55
profits and profit factors vs., 24–25,
48–51
risk–reward ratios and, 50–51, 95
RS system No. 1 and, 106
sample strategy analysis for, percent vs.
dollar amount, 51–55
TradeStation code and, 94
Risk & Portfolio Management, 329
risk adjusted return, 25
risk–reward ratio, 13, 50–51, 95, 167–171,
167, 168, 169
expert exits and, 176
filters and, 260
TWR in, 302–304
164–165
hybrid system No. 1 and, 98–99
126–127, 126, 132–133
rotation system and, 140, 144–145, 144
Sharpe ratio in, 326, 327, 343, 382
Sortino ratio in, 325, 326, 325
volume-weighted average system and,
158–159, 158, 159
robustness of system, 272
rolling time window analysis, 328, 328
rotation, 81, 137–152, 140, 220
analysis of, 138–139
evaluation of, 187
filter/filter use of, 266–269, 363–374,
363–372
lookback periods in, 140–142, 142,
145–146
moving average slope (MAS) in, 137
Index
391
rotation (continued)
risk–reward ratio in, 140, 144–145, 144
short vs. long in, 139–140, 143–146, 143,
144
stops and exits in, 139, 140, 141
test period/test data in, 138
trend filters in, 139
RS system No. 1, 81, 105–112, 220
evaluation of, 186
filter/filter use of, 344
filter/filter use of, 260–262, 261, 345–354,
346–355, 356–359, 356–359
length in trade and, 107–110
lookback in, 108–109, 108
money market strategy using, 344–359,
346–359
original rules for, 105–106
pros and cons of, 106
revising and modifying, 107–110, 107,
110
risk and, 106
risk–reward ratio in, 108–109
short vs. long term, 106
stop loss in, 107, 108
rules for systems, number of, 188–189
Russell 2000 stocks used in analysis, 84
S&P 400 Midcap stocks used in analysis, 84
S&P 500 stocks used in analysis, 84
Sharpe ratio, 326, 327, 382
short vs. long trades, 12–13
exits and, 219
expert exits and, 174, 177–178, 177
163, 165, 166
hybrid system No. 1 and, 98–99, 101–102
meander system and, 118, 119, 120
rotation system and, 139–140, 143–146,
143, 144
RS system No. 1 and, 106
154–159, 156
signals vs. trades, 43–46, 44
skew, 327–328
profit and, 23–25, 28
slow trade stop, 251, 253
hybrid system No. 1 and, 99–102, 101,
102
sorting data, TradeStation code, 91, 91
Sortino ratio, 325, 326, 325
splicing contracts, 71–75, 72, 73, 74
splits, 8
spreadsheet development, 325–342
cumulative monthly returns from, 336
distribution of drawdowns from, 335
drawdown curve from, 334
individual market summary in, 336–337,
337
initial parameter settings for, 325
money management export code for,
337–342
money management point (MMP) in, 337,
341
monthly distributions from, 335
optimal f in, 325
raw data used in, 337, 338
risk calculation in, 328–329
rolling time window analysis in, 328
Sharpe ratio in, 326, 327
skew and kurtosis in, 327–328
Sortino ratio in, 325, 326, 325
strategy summary for, 326, 327
total equity curve from, 334
spreadsheet of compiled trade results,
273–274, 274
spreadsheet using DRMM, 310–323,
311–314, 320, 321, 322
stability of system, 271–272
standard deviation, 22–25
Chebychef’s theorem and, 31
leptokurtic distributions and, 26–28, 27
platykurtic distributions and, 26–28, 27
129
132
standard error and tests for, 28–30
TradeStation code and, 93–94
trimmean function in, 30–31
standard error, profit calculation and, 28–30
start trade drawdown (STD) –65
statistics, 22–25
stocks used in analysis, 84–85
stop loss, 166–167, 251, 252, 284, 381
DRMM and, 306
Index
392
stop loss (continued)
expert exits and, 178–180, 180, 249, 249,
358–359, 358, 359, 362–366, 362, 365,
366
Harris 3L-R pattern variation and,
246–247, 246, 247, 362–363, 362,
365–366, 365, 366
hybrid system No. 1 and, 226–233,
227–233, 359–362, 360, 361
meander system and, 115, 237–240,
237–239, 345–351, 346, 347, 349, 350,
359–362, 360, 361
RS system No. 1 and, 107, 108
157, 241–242
stops (See also trailing stops), 189, 190
average true range method in, 211–212
bonus stops (uncommented), 250–254
expert exits and, 175–176, 178–182, 180,
181
max-length, 252–254
min-move, 252, 253
percent type, 209–210, 250–251
placing, 207–217
price to determine placement of,
207–208
profit protector, 251, 253
profit target, 251, 253
129–132, 132
risk amount to determine placement of,
208
rotation system and, 139, 140, 141
slow trade, 251, 253
stop loss, 251, 252
surface charts and, 212–217, 213, 214,
215, 216
trailing stop (See trailing stops)
true-range, 252
volatility-based, 210–212
157
strategy vs. system, 344
summary of data, TradeStation code, 91–92,
92
surface charts, 212–217, 213–216
exit placement and, 283–284
Sweeney, John, 65
systems as filters, 255–269
on balance volume (OBV) and, 258
profit factors and, 257–258
pros and cons of use of, 258–260
systems as filters (continued)
relative strength bands as, 262–266,
359–362, 360, 361, 366–369, 367, 368,
369, 369–374, 370, 371, 372
risk–reward ratio and, 260
rotation system as, 266–269, 363–369,
363–369, 369–374, 370, 371, 372
RS system No. 1, 260–262, 261, 344,
345–359, 346–359
trend filters and, 255–258, 256, 257
taking a profit using an exit, 203–204, 282
terminal wealth relative (TWR), 295–304,
295
time in market, 82
expert exits and, 174–175
profit calculation vs., 31–33
TradeStation code and, 94
total equity curve from spreadsheet, 334
total equity drawdown (TED), 63–65, 64
TradeStation code, 10–11, 11, 82, 83–95
compiling trade results in one spreadsheet,
273–274, 274
dynamic ratio money management
(DRMM) in, 85
EasyLanguage code in, 83–84
expert exits and, 182–183
export code in, 86–91
exported data in, 91–94, 91
futures contracts, calculate number of,
11–12
171–172
hybrid system No. 1 and, 102–103
Kelly formula in, 293
markets used in, 84
meander system and, 120–121
133–136
risk in, 94
rotation system and, 146–152
sorting data in, 91, 91
standard deviation in, 93–94
stocks used in, 84–85
summary of data in, 91–92, 92
surface chart code in, 220–226
time spent in market in, 94
159–161
trading system development, 79–82
Trading Systems Lab (See Active Trader
magazine)
Index
393
trailing stops, 251, 252–253
expert exits and, 180–182, 180, 181, 249,
250, 365–366, 365, 366
247–248, 248, 356–358, 356, 357,
362–363, 362
hybrid system No. 1 and, 233–236,
234–236, 363–365, 363, 364
meander system and, 240–241, 240,
349–351, 349, 350, 363–365, 363, 364
242–245, 243, 244, 352–356, 352,
353,355359–362, 360, 361, 363–365,
363, 364
trend filters, 186, 255–258, 256, 257
165
rotation system and, 139
155–156, 157
trimmean function, profit calculation and,
30–31
true-range stop, 252
underwater equity chart, 59, 59
DRMM and, 319, 319, 323
Van Hedge Fund Advisors, 329
variables, 271–280
consistency of system and, 272–273
equity variation over trades, 277–278, 278
loss in, 278–279, 279
robustness of system and, 272
stability of system and, 271–272
Vince, Ralph, 295, 296, 312, 380
volatility-based stops, 210–212
volume-weighted average, 80–81, 153–161
average volume (AV) in, 153
volume-weighted average (continued)
366–369, 367, 368, 369, 369–374, 370,
371, 372
entry rules in, 156
evaluation of, 186
highest average volume (HAV) in, 153
lookback period in, 155, 158–159, 158, 159
lowest average volume (LAV) in, 153
Merck trading using, 160
previous bar VMA (PVMA) in, 153–154
264–266, 264
relative value (RV) in, 153
revising and modifying, 155–159, 155, 160
risk–reward ratio in, 158–159, 158, 159
268
RS system No. 1 filter use of in, 261
short vs. long in, 154–159, 156
stop loss in, 156, 157
stop-loss version of, 241–242
244, 352–354, 352, 353, 354–356, 355,
359–365, 360, 361, 363, 364
trend filters in, 155–156, 157
winners
in a row, 38–43, 41, 42
ABOUT
THE
AUTHOR
Thomas Stridsman is a systems researcher and designer for Rotella Capital
Management, a Chicago-based commodity trading advisor with approximately $1
billion under management. A popular speaker at industry-related conferences and
seminars, Stridsman is the author of Trading Systems That Work and a longtime contributor to both Futures and Active Trader. He is a native of Sweden, where he operated a Web-based financial newsletter and trading advisory service in Stockholm
and was chair of the Swedish Technical Analyst Federation.

Trading Systems and Money Management : A Guide to Trading and

Transcription

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